JEE Main & Advanced Mathematics Inverse Trigonometric Functions Question Bank

Inverse trigonometric functions Total Questions - 137

1)

If \[{{\cos }^{-1}}\left( \frac{1}{x} \right)=\theta \], then \[\tan \theta \]= [MNR 1978; MP PET 1989]

A)
\[\frac{1}{\sqrt{{{x}^{2}}-1}}\]

B)
\[\sqrt{{{x}^{2}}+1}\]

C)
\[\sqrt{1-{{x}^{2}}}\]

D)
\[\sqrt{{{x}^{2}}-1}\]
View Solution
2)

\[\sin ({{\cot }^{-1}}x)\] [MNR 1987; MP PET 2001; DCE 2002]

A)
\[\sqrt{1+{{x}^{2}}}\]

B)
\[x\]

C)
\[{{(1+{{x}^{2}})}^{-3/2}}\]

D)
\[{{(1+{{x}^{2}})}^{-1/2}}\]
View Solution
3)

\[\cos \text{ }\left( {{\sin }^{-1}}\frac{5}{13} \right)=\]

A)
\[\frac{12}{13}\]

B)
\[-\frac{12}{13}\]

C)
\[\frac{5}{12}\]

D)
None of these
View Solution
4)

\[{{\cot }^{-1}}(-\sqrt{3})\]=

A)
\[-\frac{\pi }{6}\]

B)
\[\frac{5\pi }{6}\]

C)
\[\frac{\pi }{3}\]

D)
\[\frac{2\pi }{3}\]
View Solution
5)

\[1+{{\cot }^{2}}({{\sin }^{-1}}x)=\]

A)
\[\frac{1}{2x}\]

B)
\[{{x}^{2}}\]

C)
\[\frac{1}{{{x}^{2}}}\]

D)
\[\frac{2}{x}\]
View Solution
6)

If \[{{\sin }^{-1}}\frac{1}{2}={{\tan }^{-1}}x,\]then x =

A)
\[\sqrt{3}\]

B)
\[\frac{1}{\sqrt{3}}\]

C)
\[\frac{1}{\sqrt{2}}\]

D)
None of these
View Solution
7)

\[{{\tan }^{-1}}\left( \frac{\sqrt{1+{{x}^{2}}}-1}{x} \right)=\]

A)
\[{{\tan }^{-1}}x\]

B)
\[\frac{1}{2}{{\tan }^{-1}}x\]

C)
\[2{{\tan }^{-1}}x\]

D)
None of these
View Solution
8)

\[{{\tan }^{-1}}\frac{x}{\sqrt{{{a}^{2}}-{{x}^{2}}}}=\]

A)
\[\frac{1}{a}{{\sin }^{-1}}\left( \frac{x}{a} \right)\]

B)
\[a{{\sin }^{-1}}\left( \frac{x}{a} \right)\]

C)
\[{{\sin }^{-1}}\left( \frac{x}{a} \right)\]

D)
\[{{\sin }^{-1}}\left( \frac{a}{x} \right)\]
View Solution
9)

During \[\cos ({{\tan }^{-1}}x)=\] [MP PET 1988; MNR 1981]

A)
\[\sqrt{1+{{x}^{2}}}\]

B)
\[\frac{1}{\sqrt{1+{{x}^{2}}}}\]

C)
\[1+{{x}^{2}}\]

D)
None of these
View Solution
10)

\[\tan \left[ {{\sec }^{-1}}\sqrt{1+{{x}^{2}}} \right]=\]

A)
\[\frac{1}{x}\]

B)
x

C)
\[\frac{1}{\sqrt{1+{{x}^{2}}}}\]

D)
\[\frac{x}{\sqrt{1+{{x}^{2}}}}\]
View Solution
11)

\[{{\sec }^{-1}}[\sec (-{{30}^{o}})]=\] [MP PET 1992]

A)
\[-{{60}^{o}}\]

B)
\[-{{30}^{o}}\]

C)
\[{{30}^{o}}\]

D)
\[{{150}^{o}}\]
View Solution
12)

\[{{\tan }^{-1}}\left[ \frac{\cos x}{1+\sin x} \right]=\]

A)
\[\frac{\pi }{4}-\frac{x}{2}\]

B)
\[\frac{\pi }{4}+\frac{x}{2}\]

C)
\[\frac{x}{2}\]

D)
\[\frac{\pi }{4}-x\]
View Solution
13)

\[{{\tan }^{-1}}\frac{1}{\sqrt{{{x}^{2}}-1}}=\]

A)
\[\frac{\pi }{2}+\text{cose}{{\text{c}}^{-1}}x\]

B)
\[\frac{\pi }{2}+{{\sec }^{-1}}x\]

C)
\[\text{cose}{{\text{c}}^{-1}}x\]

D)
\[{{\sec }^{-1}}x\]
View Solution
14)

The principal value of \[{{\sin }^{-1}}\left( -\frac{1}{2} \right)\]is

A)
\[\frac{\pi }{3}\]

B)
\[\frac{\pi }{6}\]

C)
\[-\frac{\pi }{3}\]

D)
\[-\frac{\pi }{6}\]
View Solution
15)

\[{{\sec }^{2}}({{\tan }^{-1}}2)+\text{cose}{{\text{c}}^{2}}({{\cot }^{-1}}3)=\] [EAMCET 2001]

A)
5

B)
13

C)
15

D)
6
View Solution
16)

\[{{\sin }^{-1}}\left[ x\sqrt{1-x}-\sqrt{x}\sqrt{1-{{x}^{2}}} \right]=\]

A)
\[{{\sin }^{-1}}x+{{\sin }^{-1}}\sqrt{x}\]

B)
\[{{\sin }^{-1}}x-{{\sin }^{-1}}\sqrt{x}\]

C)
\[{{\sin }^{-1}}\sqrt{x}-{{\sin }^{-1}}x\]

D)
None of these
View Solution
17)

If \[{{\tan }^{-1}}\frac{1-x}{1+x}=\frac{1}{2}{{\tan }^{-1}}x\], then x =

A)
1

B)
\[\sqrt{3}\]

C)
\[\frac{1}{\sqrt{3}}\]

D)
None of these
View Solution
18)

\[{{\cos }^{-1}}\left( \cos \frac{7\pi }{6} \right)=\]

A)
\[\frac{7\pi }{6}\]

B)
\[\frac{5\pi }{6}\]

C)
\[\frac{\pi }{6}\]

D)
None of these
View Solution
19)

The value of \[\sin {{\cot }^{-1}}\tan {{\cos }^{-1}}x\]is equal to [Bihar CEE 1974]

A)
x

B)
\[\frac{\pi }{2}\]

C)
1

D)
None of these
View Solution
20)

\[{{\sin }^{-1}}\frac{\sqrt{x}}{\sqrt{x+a}}\]is equal to

A)
\[{{\cos }^{-1}}\sqrt{\frac{x}{a}}\]

B)
\[\text{cose}{{\text{c}}^{-1}}\sqrt{\frac{x}{a}}\]

C)
\[{{\tan }^{-1}}\sqrt{\frac{x}{a}}\]

D)
None of these
View Solution
21)

If \[\sin \left( {{\sin }^{-1}}\frac{1}{5}+{{\cos }^{-1}}x \right)=1\],then x is equal to [MNR 1994; Kerala (Engg.) 2005]

A)
1

B)
0

C)
\[\frac{4}{5}\]

D)
\[\frac{1}{5}\]
View Solution
22)

If \[{{\sin }^{-1}}x=\theta +\beta \]and \[{{\sin }^{-1}}y=\theta -\beta ,\]then \[1+xy=\]

A)
\[{{\sin }^{2}}\theta +{{\sin }^{2}}\beta \]

B)
\[{{\sin }^{2}}\theta +{{\cos }^{2}}\beta \]

C)
\[{{\cos }^{2}}\theta +{{\cos }^{2}}\beta \]

D)
\[{{\cos }^{2}}\theta +{{\sin }^{2}}\beta \]
View Solution
23)

If \[{{\sin }^{-1}}\frac{1}{3}+{{\sin }^{-1}}\frac{2}{3}={{\sin }^{-1}}x,\]then x is equal to [Roorkee 1995]

A)
0

B)
\[\frac{\sqrt{5}-4\sqrt{2}}{9}\]

C)
\[\frac{\sqrt{5}+4\sqrt{2}}{9}\]

D)
\[\frac{\pi }{2}\]
View Solution
24)

\[\tan ({{\cos }^{-1}}x)\] is equal to [IIT 1993]

A)
\[\frac{\sqrt{1-{{x}^{2}}}}{x}\]

B)
\[\frac{x}{1+{{x}^{2}}}\]

C)
\[\frac{\sqrt{1+{{x}^{2}}}}{x}\]

D)
\[\sqrt{1-{{x}^{2}}}\]
View Solution
25)

The domain of \[{{\sin }^{-1}}x\]is [Roorkee 1993]

A)
\[(-\pi ,\pi )\]

B)
[-1, 1]

C)
\[(0,\,2\pi )\]

D)
\[(-\infty ,\,\infty )\]
View Solution
26)

The principal value of \[{{\sin }^{-1}}\left( -\,\,\frac{\sqrt{3}}{2} \right)\]is [Roorkee 1992]

A)
\[\frac{-2\pi }{3}\]

B)
\[\frac{-\pi }{3}\]

C)
\[\frac{-2\pi }{3}\]

D)
\[\frac{5\pi }{3}\]
View Solution
27)

\[\cot \,\,\left[ {{\cos }^{-1}}\left( \frac{7}{25} \right) \right]=\] [Karnataka CET 1994]

A)
\[\frac{25}{24}\]

B)
\[\frac{25}{7}\]

C)
\[\frac{24}{25}\]

D)
None of these
View Solution
28)

If \[\frac{\pi }{2}\le x\le \frac{3\pi }{2},\]then\[{{\sin }^{-1}}(\sin x)\]is equal to

A)
x

B)
\[-x\]

C)
\[\pi +x\]

D)
\[\pi -x\]
View Solution
29)

If \[\pi \le x\le 2\pi \], then \[{{\cos }^{-1}}(\cos x)\]is equal to

A)
x

B)
\[-x\]

C)
\[2\pi +x\]

D)
\[2\pi -x\]
View Solution
30)

The value of \[{{\sin }^{-1}}(\sin 10)\]is

A)
10

B)
\[10-3\pi \]

C)
\[3\pi -10\]

D)
None of these
View Solution
31)

The smallest and the largest values of \[{{\tan }^{-1}}\left( \frac{1-x}{1+x} \right)\text{ },\,\,0\le x\le 1\]are

A)
\[0,\,\,\pi \]

B)
\[0,\,\frac{\pi }{4}\]

C)
\[-\frac{\pi }{4},\frac{\pi }{4}\]

D)
\[\frac{\pi }{4},\,\frac{\pi }{2}\]
View Solution
32)

If \[x\]takes non-positive permissible value, then \[{{\sin }^{-1}}x\]=

A)
\[{{\cos }^{-1}}\sqrt{1-{{x}^{2}}}\]

B)
\[-{{\cos }^{-1}}\sqrt{1-{{x}^{2}}}\]

C)
\[{{\cos }^{-1}}\sqrt{{{x}^{2}}-1}\]

D)
\[\pi -{{\cos }^{-1}}\sqrt{1-{{x}^{2}}}\]
View Solution
33)

\[{{\left[ \sin \left( {{\tan }^{-1}}\frac{3}{4} \right) \right]}^{2}}=\] [EAMCET 1983]

A)
\[\frac{3}{5}\]

B)
\[\frac{5}{3}\]

C)
\[\frac{9}{25}\]

D)
\[\frac{25}{9}\]
View Solution
34)

The principal value of \[{{\sin }^{-1}}\left( \sin \frac{5\pi }{3} \right)\]is [MP PET 1996]

A)
\[\frac{5\pi }{3}\]

B)
\[-\frac{5\pi }{3}\]

C)
\[-\frac{\pi }{3}\]

D)
\[\frac{4\pi }{3}\]
View Solution
35)

The value of x which satisfies the equation \[{{\tan }^{-1}}x=\] \[{{\sin }^{-1}}\left( \frac{3}{\sqrt{10}} \right)\] is [Pb. CET 1999]

A)
3

B)
-3

C)
\[\frac{1}{3}\]

D)
\[-\frac{1}{3}\]
View Solution
36)

\[\sec (\text{cose}{{\text{c}}^{-1}}x)\] is equal to [Kurukshetra CEE 2001]

A)
\[\text{cosec}({{\sec }^{-1}}x)\]

B)
\[\cot x\]

C)
\[\pi \]

D)
None of these
View Solution
37)

The range of \[{{\tan }^{-1}}\]x is [DCE 2002]

A)
\[\left( \pi ,\frac{\pi }{2} \right)\]

B)
\[\left( -\frac{\pi }{2},\frac{\pi }{2} \right)\]

C)
\[(-\pi ,\,\,\pi )\]

D)
\[(0,\pi )\]
View Solution
38)

If \[\theta ={{\sin }^{-1}}[\sin (-{{600}^{o}})]\], then one of the possible value of \[\theta \]is [Kerala (Engg.) 2002]

A)
\[\frac{\pi }{3}\]

B)
\[\frac{\pi }{2}\]

C)
\[\frac{2\pi }{3}\]

D)
\[\frac{-2\pi }{3}\]
View Solution
39)

The solution set of the equation \[{{\sin }^{-1}}x=2{{\tan }^{-1}}x\] is [AMU 2002]

A)
{1, 2}

B)
{-1, 2}

C)
{-1, 1, 0}

D)
{1, 1/2, 0}
View Solution
40)

The value of \[\cos ({{\tan }^{-1}}(\tan 2))\]is [AMU 2002]

A)
\[\frac{1}{\sqrt{5}}\]

B)
\[-\frac{1}{\sqrt{5}}\]

C)
\[\cos \,2\]

D)
\[-\cos 2\]
View Solution
41)

If \[{{\sin }^{-1}}x+{{\sin }^{-1}}y+{{\sin }^{-1}}z=\frac{\pi }{2}\], then the value of \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}+2xyz\]is equal to [Pb. CET 2002]

A)
0

B)
1

C)
2

D)
3
View Solution
42)

\[\sin \left[ \frac{\pi }{2}-{{\sin }^{-1}}\left( -\frac{\sqrt{3}}{2} \right) \right]=\]

A)
\[\frac{\sqrt{3}}{2}\]

B)
\[-\frac{\sqrt{3}}{2}\]

C)
\[\frac{1}{2}\]

D)
\[-\frac{1}{2}\]
View Solution
43)

\[\sin [{{\cot }^{-1}}(\cos {{\tan }^{-1}}x)]\]=

A)
\[\frac{x}{\sqrt{{{x}^{2}}+2}}\]

B)
\[\frac{x}{\sqrt{{{x}^{2}}+1}}\]

C)
\[\frac{1}{\sqrt{{{x}^{2}}+2}}\]

D)
\[\sqrt{\frac{{{x}^{2}}+1}{{{x}^{2}}+2}}\]
View Solution
44)

If \[\sin ({{\cot }^{-1}}(x+1)=\cos ({{\tan }^{-1}}x)\], then x = [IIT Screening 2004]

A)
\[-\frac{1}{2}\]

B)
\[\frac{1}{2}\]

C)
0

D)
\[\frac{9}{4}\]
View Solution
45)

\[{{\cos }^{-1}}\frac{4}{5}+{{\tan }^{-1}}\frac{3}{5}=\]

A)
\[{{\tan }^{-1}}\frac{27}{11}\]

B)
\[{{\sin }^{-1}}\frac{11}{27}\]

C)
\[{{\cos }^{-1}}\frac{11}{27}\]

D)
None of these
View Solution
46)

\[{{\sin }^{-1}}x+{{\sin }^{-1}}\frac{1}{x}+{{\cos }^{-1}}x+{{\cos }^{-1}}\frac{1}{x}=\]

A)
\[\pi \]

B)
\[\frac{\pi }{2}\]

C)
\[\frac{3\pi }{2}\]

D)
None of these
View Solution
47)

\[2{{\tan }^{-1}}\frac{1}{3}+{{\tan }^{-1}}\frac{1}{2}=\]

A)
\[{{90}^{o}}\]

B)
\[{{60}^{o}}\]

C)
\[{{45}^{o}}\]

D)
\[{{\tan }^{-1}}2\]
View Solution
48)

\[\tan \left( {{90}^{o}}-{{\cot }^{-1}}\frac{1}{3} \right)=\]

A)
3

B)
\[\frac{2}{3}\]

C)
\[\frac{1}{3}\]

D)
\[\frac{1}{\sqrt{10}}\]
View Solution
49)

\[\tan \left[ {{\cos }^{-1}}\frac{4}{5}+{{\tan }^{-1}}\frac{2}{3} \right]\]= [IIT 1983; EAMCET 1988; MP PET 1990; MNR 1992]

A)
6/17

B)
17/6

C)
7/16

D)
16/7
View Solution
50)

\[{{\tan }^{-1}}1+{{\tan }^{-1}}2+{{\tan }^{-1}}3=\]

A)
\[\frac{\pi }{2}\]

B)
\[\frac{\pi }{4}\]

C)
0

D)
None of these
View Solution
51)

\[{{\cot }^{-1}}\frac{3}{4}+{{\sin }^{-1}}\frac{5}{13}=\]

A)
\[{{\sin }^{-1}}\frac{63}{65}\]

B)
\[{{\sin }^{-1}}\frac{12}{13}\]

C)
\[{{\sin }^{-1}}\frac{65}{68}\]

D)
\[{{\sin }^{-1}}\frac{5}{12}\]
View Solution
52)

If \[{{\cos }^{-1}}x+{{\cos }^{-1}}y+{{\cos }^{-1}}z=\pi \], then [Roorkee 1994]

A)
\[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}+xyz=0\]

B)
\[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}+2xyz=0\]

C)
\[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}+xyz=1\]

D)
\[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}+2xyz=1\]
View Solution
53)

If \[{{\tan }^{-1}}x-{{\tan }^{-1}}y={{\tan }^{-1}}A,\]then A = [MP PET 1988]

A)
\[x-y\]

B)
\[x+y\]

C)
\[\frac{x-y}{1+xy}\]

D)
\[\frac{x+y}{1-xy}\]
View Solution
54)

If \[{{\tan }^{-1}}x+{{\tan }^{-1}}y+{{\tan }^{-1}}z=\frac{\pi }{2},\]then [Karnataka CET 1996]

A)
\[x+y+z-xyz=0\]

B)
\[x+y+z+xyz=0\]

C)
\[xy+yz+zx+1=0\]

D)
\[xy+yz+zx-1=0\]
View Solution
55)

If \[{{\tan }^{-1}}\frac{x-1}{x+2}+{{\tan }^{-1}}\frac{x+1}{x+2}=\frac{\pi }{4}\], then x =

A)
\[\frac{1}{\sqrt{2}}\]

B)
\[-\frac{1}{\sqrt{2}}\]

C)
\[\pm \sqrt{\frac{5}{2}}\]

D)
\[\pm \frac{1}{2}\]
View Solution
56)

\[{{\cos }^{-1}}\sqrt{1-x}+{{\sin }^{-1}}\sqrt{1-x}=\]

A)
\[\pi \]

B)
\[\frac{\pi }{2}\]

C)
1

D)
0
View Solution
57)

\[\cos \left[ 2{{\cos }^{-1}}\frac{1}{5}+{{\sin }^{-1}}\frac{1}{5} \right]=\] [IIT 1981]

A)
\[\frac{2\sqrt{6}}{5}\]

B)
\[-\frac{2\sqrt{6}}{5}\]

C)
\[\frac{1}{5}\]

D)
\[-\frac{1}{5}\]
View Solution
58)

\[{{\tan }^{-1}}\frac{a-b}{1+ab}+{{\tan }^{-1}}\frac{b-c}{1+bc}=\]

A)
\[{{\tan }^{-1}}a-{{\tan }^{-1}}b\]

B)
\[{{\tan }^{-1}}a-{{\tan }^{-1}}c\]

C)
\[{{\tan }^{-1}}b-{{\tan }^{-1}}c\]

D)
\[{{\tan }^{-1}}c-{{\tan }^{-1}}a\]
View Solution
59)

If \[{{\tan }^{-1}}2x+{{\tan }^{-1}}3x=\frac{\pi }{4}\], then x = [Roorkee 1978, 80; MNR 1986; Pb. CET 2001; Karnataka CET 2002]

A)
- 1

B)
\[\frac{1}{6}\]

C)
\[-1,\,\frac{1}{6}\]

D)
None of these
View Solution
60)

If \[{{\cot }^{-1}}x+{{\tan }^{-1}}3=\frac{\pi }{2}\], then x =

A)
1/3

B)
1/4

C)
3

D)
4
View Solution
61)

\[2{{\sin }^{-1}}\frac{3}{5}+{{\cos }^{-1}}\frac{24}{25}=\]

A)
\[\frac{\pi }{2}\]

B)
\[\frac{2\pi }{3}\]

C)
\[\frac{5\pi }{3}\]

D)
None of these
View Solution
62)

\[\cos \left[ {{\tan }^{-1}}\frac{1}{3}+{{\tan }^{-1}}\frac{1}{2} \right]=\] [MP PET 1991; MNR 1990]

A)
\[\frac{1}{\sqrt{2}}\]

B)
\[\frac{\sqrt{3}}{2}\]

C)
\[\frac{1}{2}\]

D)
\[\frac{\pi }{4}\]
View Solution
63)

\[{{\tan }^{-1}}x+{{\cot }^{-1}}(x+1)=\]

A)
\[{{\tan }^{-1}}({{x}^{2}}+1)\]

B)
\[{{\tan }^{-1}}({{x}^{2}}+x)\]

C)
\[{{\tan }^{-1}}(x+1)\]

D)
\[{{\tan }^{-1}}({{x}^{2}}+x+1)\]
View Solution
64)

\[{{\cot }^{-1}}\frac{xy+1}{x-y}+{{\cot }^{-1}}\frac{yz+1}{y-z}+{{\cot }^{-1}}\frac{zx+1}{z-x}=\]

A)
0

B)
1

C)
\[{{\cot }^{-1}}x+{{\cot }^{-1}}y+{{\cot }^{-1}}z\]

D)
None of these
View Solution
65)

If \[{{\tan }^{-1}}\frac{a+x}{a}+{{\tan }^{-1}}\frac{a-x}{a}=\frac{\pi }{6}\],then \[{{x}^{2}}\]=

A)
\[2\sqrt{3}a\]

B)
\[\sqrt{3}a\]

C)
\[2\sqrt{3}{{a}^{2}}\]

D)
None of these
View Solution
66)

If \[{{\cos }^{-1}}\frac{3}{5}-{{\sin }^{-1}}\frac{4}{5}={{\cos }^{-1}}x,\]then x = [AMU 1978]

A)
0

B)
1

C)
-1

D)
2
View Solution
67)

\[{{\cot }^{-1}}3+\text{cose}{{\text{c}}^{-1}}\sqrt{5}\]=

A)
\[\frac{\pi }{3}\]

B)
\[\frac{\pi }{4}\]

C)
\[\frac{\pi }{6}\]

D)
\[\frac{\pi }{2}\]
View Solution
68)

\[{{\tan }^{-1}}\frac{1-{{x}^{2}}}{2x}+{{\cos }^{-1}}\frac{1-{{x}^{2}}}{1+{{x}^{2}}}=\]

A)
\[\frac{\pi }{4}\]

B)
\[\frac{\pi }{2}\]

C)
\[\pi \]

D)
0
View Solution
69)

If \[{{\tan }^{-1}}(x-1)+{{\tan }^{-1}}x+{{\tan }^{-1}}(x+1)={{\tan }^{-1}}3x\],then x =

A)
\[\pm \frac{1}{2}\]

B)
\[0,\,\frac{1}{2}\]

C)
\[0,\,-\frac{1}{2}\]

D)
\[0,\,\pm \frac{1}{2}\]
View Solution
70)

If \[{{\cos }^{-1}}x+{{\cos }^{-1}}y=2\pi ,\]then \[{{\sin }^{-1}}x+{{\sin }^{-1}}y\]is equal to

A)
\[\pi \]

B)
\[-\pi \]

C)
\[\frac{\pi }{2}\]

D)
None of these
View Solution
71)

\[{{\sin }^{-1}}\frac{1}{\sqrt{5}}+{{\cot }^{-1}}3\]is equal to [MP PET 1993; Karnataka CET 1995]

A)
\[\frac{\pi }{6}\]

B)
\[\frac{\pi }{4}\]

C)
\[\frac{\pi }{3}\]

D)
\[\frac{\pi }{2}\]
View Solution
72)

If \[{{\cot }^{-1}}\alpha +{{\cot }^{-1}}\beta ={{\cot }^{-1}}x,\]then \[x=\] [MP PET 1992]

A)
\[\alpha +\beta \]

B)
\[\alpha -\beta \]

C)
\[\frac{1+\alpha \beta }{\alpha +\beta }\]

D)
\[\frac{\alpha \beta -1}{\alpha +\beta }\]
View Solution
73)

If \[{{\sin }^{-1}}\left( \frac{2a}{1+{{a}^{2}}} \right)+{{\sin }^{-1}}\left( \frac{2b}{1+{{b}^{2}}} \right)=2{{\tan }^{-1}}x,\]then \[x=\] [MNR 1984; UPSEAT 1999; Pb. CET 2004]

A)
\[\frac{a-b}{1+ab}\]

B)
\[\frac{b}{1+ab}\]

C)
\[\frac{b}{1-ab}\]

D)
\[\frac{a+b}{1-ab}\]
View Solution
74)

\[{{\cos }^{-1}}\frac{1}{2}+2{{\sin }^{-1}}\frac{1}{2}\]is equal to [MP PET 1998; UPSEAT 2004]

A)
\[\frac{\pi }{4}\]

B)
\[\frac{\pi }{6}\]

C)
\[\frac{\pi }{3}\]

D)
\[\frac{2\pi }{3}\]
View Solution
75)

\[{{\tan }^{-1}}\frac{3}{4}+{{\tan }^{-1}}\frac{3}{5}-{{\tan }^{-1}}\frac{8}{19}=\] [AMU 1976, 77]

A)
\[\frac{\pi }{4}\]

B)
\[\frac{\pi }{3}\]

C)
\[\frac{\pi }{6}\]

D)
None of these
View Solution
76)

\[4{{\tan }^{-1}}\frac{1}{5}-{{\tan }^{-1}}\frac{1}{70}+{{\tan }^{-1}}\frac{1}{99}=\] [Roorkee 1981]

A)
\[\frac{\pi }{2}\]

B)
\[\frac{\pi }{3}\]

C)
\[\frac{\pi }{4}\]

D)
None of these
View Solution
77)

If \[{{\sin }^{-1}}x+{{\sin }^{-1}}y=\frac{2\pi }{3},\]then \[{{\cos }^{-1}}x+{{\cos }^{-1}}y=\] [EAMCET 1994]

A)
\[\frac{2\pi }{3}\]

B)
\[\frac{\pi }{3}\]

C)
\[\frac{\pi }{6}\]

D)
\[\pi \]
View Solution
78)

\[{{\tan }^{-1}}\left( \frac{1}{4} \right)+{{\tan }^{-1}}\left( \frac{2}{9} \right)=\] [EAMCET 1994]

A)
\[\frac{1}{2}{{\cos }^{-1}}\left( \frac{3}{5} \right)\]

B)
\[\frac{1}{2}{{\sin }^{-1}}\left( \frac{3}{5} \right)\]

C)
\[\frac{1}{2}{{\tan }^{-1}}\left( \frac{3}{5} \right)\]

D)
\[{{\tan }^{-1}}\left( \frac{1}{2} \right)\]
View Solution
79)

\[{{\tan }^{-1}}\left( \frac{x}{y} \right)-{{\tan }^{-1}}\,\left( \frac{x-y}{x+y} \right)\] is [EAMCET 1992]

A)
\[\frac{\pi }{2}\]

B)
\[\frac{\pi }{3}\]

C)
\[\frac{\pi }{4}\]

D)
\[\frac{\pi }{4}\]or \[-\frac{3\pi }{4}\]
View Solution
80)

If \[{{\sin }^{-1}}\frac{x}{5}+\text{cose}{{\text{c}}^{-1}}\left( \frac{5}{4} \right)=\frac{\pi }{2},\]then \[x=\] [EAMCET 1983; Karnataka CET 2004]

A)
4

B)
5

C)
1

D)
3
View Solution
81)

\[2{{\tan }^{-1}}\left( \frac{1}{3} \right)+{{\tan }^{-1}}\left( \frac{1}{7} \right)=\] [EAMCET 1983]

A)
\[{{\tan }^{-1}}\left( \frac{49}{29} \right)\]

B)
\[\frac{\pi }{2}\]

C)
0

D)
\[\frac{\pi }{4}\]
View Solution
82)

\[{{\cos }^{-1}}\left( \frac{15}{17} \right)+2{{\tan }^{-1}}\left( \frac{1}{5} \right)=\] [EAMCET 1981]

A)
\[\frac{\pi }{2}\]

B)
\[{{\cos }^{-1}}\left( \frac{171}{221} \right)\]

C)
\[\frac{\pi }{4}\]

D)
None of these
View Solution
83)

\[{{\sin }^{-1}}\left( \frac{3}{5} \right)+{{\tan }^{-1}}\left( \frac{1}{7} \right)=\] [Karnataka CET 1994]

A)
\[\frac{\pi }{4}\]

B)
\[\frac{\pi }{2}\]

C)
\[{{\cos }^{-1}}\left( \frac{4}{5} \right)\]

D)
\[\pi \]
View Solution
84)

A solution of the equation \[{{\tan }^{-1}}(1+x)\] \[+{{\tan }^{-1}}(1-x)\] \[=\frac{\pi }{2}\] is [Karnataka CET 1993]

A)
\[x=1\]

B)
\[x=-1\]

C)
\[x=0\]

D)
\[x=\pi \]
View Solution
85)

If \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}={{r}^{2}}\], then\[{{\tan }^{-1}}\left( \frac{xy}{zr} \right)+\] \[{{\tan }^{-1}}\left( \frac{yz}{xr} \right)+\tan \left( \frac{zx}{yr} \right)=\]

A)
\[\pi \]

B)
\[\frac{\pi }{2}\]

C)
0

D)
None of these
View Solution
86)

The greatest and the least value of \[{{({{\sin }^{-1}}x)}^{3}}+{{({{\cos }^{-1}}x)}^{3}}\]are

A)
\[-\frac{\pi }{2},\,\frac{\pi }{2}\]

B)
\[-\frac{{{\pi }^{3}}}{8},\,\frac{{{\pi }^{3}}}{8}\]

C)
\[\frac{7{{\pi }^{3}}}{8},\,\,\frac{{{\pi }^{3}}}{32}\]

D)
None of these
View Solution
87)

If \[a<\frac{1}{32},\] then the number of solution of \[{{({{\sin }^{-1}}x)}^{3}}+{{({{\cos }^{-1}}x)}^{3}}=a{{\pi }^{3}}\] is

A)
0

B)
1

C)
2

D)
Infinite
View Solution
88)

If \[k\le {{\sin }^{-1}}x+{{\cos }^{-1}}x+{{\tan }^{-1}}x\le K,\]then

A)
\[k=0,\,K=\pi \]

B)
\[k=0,K=\frac{\pi }{2}\]

C)
\[k=\frac{\pi }{2},K=\pi \]

D)
None of these
View Solution
89)

If \[{{({{\tan }^{-1}}x)}^{2}}+{{({{\cot }^{-1}}x)}^{2}}=\frac{5{{\pi }^{2}}}{8},\]then \[x\] equals

A)
-1

B)
1

C)
0

D)
None of these
View Solution
90)

If \[\tan (x+y)=33\]and \[x={{\tan }^{-1}}3,\]then y will be

A)
\[0.3\]

B)
\[{{\tan }^{-1}}(1.3)\]

C)
\[{{\tan }^{-1}}(0.3)\]

D)
\[{{\tan }^{-1}}\left( \frac{1}{18} \right)\]
View Solution
91)

If \[{{\tan }^{-1}}\frac{x-1}{x+1}+{{\tan }^{-1}}\frac{2x-1}{2x+1}={{\tan }^{-1}}\frac{23}{36},\]then x = [ISM Dhanbad 1973]

A)
\[\frac{3}{4},\frac{-3}{8}\]

B)
\[\frac{3}{4},\frac{3}{8}\]

C)
\[\frac{4}{3},\frac{3}{8}\]

D)
None of these
View Solution
92)

\[{{\tan }^{-1}}\frac{{{c}_{1}}x-y}{{{c}_{1}}y+x}+{{\tan }^{-1}}\frac{{{c}_{2}}-{{c}_{1}}}{1+{{c}_{2}}{{c}_{1}}}+\]\[{{\tan }^{-1}}\frac{{{c}_{3}}-{{c}_{2}}}{1+{{c}_{3}}{{c}_{2}}}+...+{{\tan }^{-1}}\frac{1}{{{c}_{n}}}=\]

A)
\[{{\tan }^{-1}}\frac{y}{x}\]

B)
\[{{\tan }^{-1}}yx\]

C)
\[{{\tan }^{-1}}\frac{x}{y}\]

D)
\[{{\tan }^{-1}}(x-y)\]
View Solution
93)

\[\sin \left\{ {{\sin }^{-1}}\frac{1}{2}+{{\cos }^{-1}}\frac{1}{2} \right\}=\] [EAMCET 1985]

A)
0

B)
-1

C)
2

D)
1
View Solution
94)

\[{{\sin }^{-1}}\frac{4}{5}+2{{\tan }^{-1}}\frac{1}{3}=\] [ISM Dhanbad 1971]

A)
\[\frac{\pi }{2}\]

B)
\[\frac{\pi }{3}\]

C)
\[\frac{\pi }{4}\]

D)
None of these
View Solution
95)

\[{{\sin }^{-1}}x+{{\cos }^{-1}}x\] is equal to [Pb. CET 1997; DCE 2002]

A)
\[\frac{\pi }{4}\]

B)
\[\frac{\pi }{2}\]

C)
-1

D)
1
View Solution
96)

\[{{\tan }^{-1}}\frac{1}{2}+{{\tan }^{-1}}\frac{1}{3}\]= [MP PET 1997, 2003; UPSEAT 2000; Karnataka CET 2001; Pb. CET 2004]

A)
0

B)
\[\pi /4\]

C)
\[\pi /2\]

D)
\[\pi \]
View Solution
97)

\[{{\tan }^{-1}}\left( \frac{1}{11} \right)+{{\tan }^{-1}}\left( \frac{2}{12} \right)=\] [DCE 1999]

A)
\[{{\tan }^{-1}}\left( \frac{33}{132} \right)\]

B)
\[{{\tan }^{-1}}\left( \frac{1}{2} \right)\]

C)
\[{{\tan }^{-1}}\left( \frac{132}{33} \right)\]

D)
None of these
View Solution
98)

If \[{{\tan }^{-1}}x+2{{\cot }^{-1}}x=\frac{2\pi }{3},\]then x = [Karnataka CET 1999]

A)
\[\sqrt{2}\]

B)
3

C)
\[\sqrt{3}\]

D)
\[\frac{\sqrt{3}-1}{\sqrt{3}+1}\]
View Solution
99)

If \[{{\sin }^{-1}}x+{{\cot }^{-1}}\left( \frac{1}{2} \right)=\frac{\pi }{2},\]then x is [Roorkee 1999; Karnataka CET 1999]

A)
0

B)
\[\frac{1}{\sqrt{5}}\]

C)
\[\frac{2}{\sqrt{5}}\]

D)
\[\frac{\sqrt{3}}{2}\]
View Solution
100)

If \[{{\sin }^{-1}}a+{{\sin }^{-1}}b+{{\sin }^{-1}}c=\pi ,\] then the value of \[a\sqrt{(1-{{a}^{2}})}+b\sqrt{(1-{{b}^{2}})}+c\sqrt{(1-{{c}^{2}})}\] will be [UPSEAT 1999]

A)
\[2abc\]

B)
\[abc\]

C)
\[\frac{1}{2}abc\]

D)
\[\frac{1}{3}abc\]
View Solution
101)

The value of \[{{\cos }^{-1}}\left( \cos \frac{5\pi }{3} \right)+{{\sin }^{-1}}\left( \sin \frac{5\pi }{3} \right)\]is [Roorkee 2000]

A)
0

B)
\[\frac{\pi }{2}\]

C)
\[\frac{2\pi }{3}\]

D)
\[\frac{10\pi }{3}\]
View Solution
102)

If \[4{{\sin }^{-1}}x+{{\cos }^{-1}}x=\pi ,\]then\[x\]is equal to [UPSEAT 2001]

A)
0

B)
\[\frac{1}{2}\]

C)
\[-\frac{\sqrt{3}}{2}\]

D)
\[\frac{1}{\sqrt{2}}\]
View Solution
103)

If \[{{\sin }^{-1}}\frac{3}{5}+{{\cos }^{-1}}\left( \frac{12}{13} \right)={{\sin }^{-1}}C,\]then C = [Pb. CET 1999]

A)
\[\frac{65}{56}\]

B)
\[\frac{24}{65}\]

C)
\[\frac{16}{65}\]

D)
\[\frac{56}{65}\]
View Solution
104)

\[\sin \left\{ {{\tan }^{-1}}\left( \frac{1-{{x}^{2}}}{2x} \right)+{{\cos }^{-1}}\left( \frac{1-{{x}^{2}}}{1+{{x}^{2}}} \right) \right\}\]is equal to [Kurukshetra CEE 2001]

A)
0

B)
1

C)
\[\sqrt{2}\]

D)
\[\frac{1}{\sqrt{2}}\]
View Solution
105)

The value of \[{{\cos }^{-1}}\left( \cos \frac{5\pi }{3} \right)+{{\sin }^{-1}}\left( \cos \frac{5\pi }{3} \right)\]is [UPSEAT 2003]

A)
\[\frac{\pi }{2}\]

B)
\[\frac{5\pi }{3}\]

C)
\[\frac{10\pi }{3}\]

D)
\[0\]
View Solution
106)

The value of \[{{\sin }^{-1}}\left( \frac{\sqrt{3}}{2} \right)-{{\sin }^{-1}}\left( \frac{1}{2} \right)\]is [MP PET 2003]

A)
\[{{45}^{o}}\]

B)
\[{{90}^{o}}\]

C)
\[{{15}^{o}}\]

D)
\[{{30}^{o}}\]
View Solution
107)

If \[{{\cos }^{-1}}x+{{\cos }^{-1}}y+{{\cos }^{-1}}z=3\pi ,\]then \[xy+yz+zx=\] [Karnataka CET 2003]

A)
0

B)
1

C)
3

D)
-3
View Solution
108)

\[\cos \text{ }\left[ {{\cos }^{-1}}\text{ }\left( \frac{-1}{7} \right)+{{\sin }^{-1}}\text{ }\left( \frac{-1}{7} \right) \right]=\] [EAMCET 2003]

A)
\[-1/3\]

B)
0

C)
\[1/3\]

D)
\[4/9\]
View Solution
109)

The value of \[\tan \left[ {{\sin }^{-1}}\left( \frac{3}{5} \right)+{{\cos }^{-1}}\left( \frac{3}{\sqrt{13}} \right) \right]\]is [AMU 2001]

A)
\[\frac{6}{17}\]

B)
\[\frac{6}{\sqrt{13}}\]

C)
\[\frac{\sqrt{13}}{5}\]

D)
\[\frac{17}{6}\]
View Solution
110)

The value of \[\tan \left( {{\tan }^{-1}}\frac{1}{2}-{{\tan }^{-1}}\frac{1}{3} \right)\]is [AMU 2001]

A)
\[5/6\]

B)
\[7/6\]

C)
\[1/6\]

D)
\[1/7\]
View Solution
111)

If \[{{\cos }^{-1}}\sqrt{p}+{{\cos }^{-1}}\sqrt{1-p}+{{\cos }^{-1}}\sqrt{1-q}=\frac{3\pi }{4},\] then the value of q is [Karnataka CET 2002; Pb. CET 2000]

A)
1

B)
\[\frac{1}{\sqrt{2}}\]

C)
\[\frac{1}{3}\]

D)
\[\frac{1}{2}\]
View Solution
112)

\[{{\cot }^{-1}}[{{(\cos \alpha )}^{1/2}}]-{{\tan }^{-1}}[{{(\cos \alpha )}^{1/2}}]=x,\]then \[\sin x=\] [AIEEE 2002]

A)
\[{{\tan }^{2}}\left( \frac{\alpha }{2} \right)\]

B)
\[{{\cot }^{2}}\left( \frac{\alpha }{2} \right)\]

C)
\[\tan \alpha \]

D)
\[\cot \left( \frac{\alpha }{2} \right)\]
View Solution
113)

If \[{{\tan }^{-1}}x+{{\tan }^{-1}}y+{{\tan }^{-1}}z=\pi ,\] then \[\frac{1}{xy}+\frac{1}{yz}+\frac{1}{zx}=\] [MP PET 1991]

A)
0

B)
1

C)
\[\frac{1}{xyz}\]

D)
\[xyz\]
View Solution
114)

\[\tan \left[ \frac{1}{2}{{\sin }^{-1}}\left( \frac{2a}{1+{{a}^{2}}} \right)+\frac{1}{2}{{\cos }^{-1}}\left( \frac{1-{{a}^{2}}}{1+{{a}^{2}}} \right) \right]=\]

A)
\[\frac{2a}{1+{{a}^{2}}}\]

B)
\[\frac{1-{{a}^{2}}}{1+{{a}^{2}}}\]

C)
\[\frac{2a}{1-{{a}^{2}}}\]

D)
None of these
View Solution
115)

If \[A={{\tan }^{-1}}x\], then \[\sin 2A=\] [MNR 1988; UPSEAT 2000]

A)
\[\frac{2x}{\sqrt{1-{{x}^{2}}}}\]

B)
\[\frac{2x}{1-{{x}^{2}}}\]

C)
\[\frac{2x}{1+{{x}^{2}}}\]

D)
None of these
View Solution
116)

If \[\cos (2{{\sin }^{-1}}x)=\frac{1}{9},\]then \[x=\] [Roorkee 1975]

A)
Only 2/3

B)
Only -2/3

C)
2/3, -2/3

D)
Neither 2/3 nor -2/3
View Solution
117)

If \[2{{\tan }^{-1}}(\cos x)={{\tan }^{-1}}(2\text{cosec }x),\] then x =

A)
\[\frac{3\pi }{4}\]

B)
\[\frac{\pi }{4}\]

C)
\[\frac{\pi }{3}\]

D)
None of these
View Solution
118)

\[\tan \left( 2{{\cos }^{-1}}\frac{3}{5} \right)=\]

A)
\[\frac{7}{25}\]

B)
\[\frac{24}{25}\]

C)
\[-\frac{24}{7}\]

D)
\[\frac{8}{3}\]
View Solution
119)

\[\tan \left[ 2{{\tan }^{-1}}\left( \frac{1}{5} \right)-\frac{\pi }{4} \right]=\] [IIT 1984]

A)
\[\frac{17}{7}\]

B)
\[-\frac{17}{7}\]

C)
\[\frac{7}{17}\]

D)
\[-\frac{7}{17}\]
View Solution
120)

If \[2{{\cos }^{-1}}\sqrt{\frac{1+x}{2}}=\frac{\pi }{2},\]then \[x=\]

A)
1

B)
0

C)
-1/2

D)
1/2
View Solution
121)

\[\tan \left[ \frac{1}{2}{{\cos }^{-1}}\left( \frac{\sqrt{5}}{3} \right) \right]=\] [Roorkee 1986]

A)
\[\frac{3-\sqrt{5}}{2}\]

B)
\[\frac{3+\sqrt{5}}{2}\]

C)
\[\frac{2}{3-\sqrt{5}}\]

D)
\[\frac{2}{3+\sqrt{5}}\]
View Solution
122)

\[\frac{1}{2}{{\cos }^{-1}}\left( \frac{1-x}{1+x} \right)=\]

A)
\[{{\cot }^{-1}}\sqrt{x}\]

B)
\[{{\tan }^{-1}}\sqrt{x}\]

C)
\[{{\tan }^{-1}}x\]

D)
\[{{\cot }^{-1}}x\]
View Solution
123)

\[\sin \left( 4{{\tan }^{-1}}\frac{1}{3} \right)=\]

A)
\[\frac{12}{25}\]

B)
\[\frac{24}{25}\]

C)
\[\frac{1}{5}\]

D)
None of these
View Solution
124)

\[3{{\tan }^{-1}}a\]is equal to [MP PET 1993]

A)
\[{{\tan }^{-1}}\frac{3a+{{a}^{3}}}{1+3{{a}^{2}}}\]

B)
\[{{\tan }^{-1}}\frac{3a-{{a}^{3}}}{1+3{{a}^{2}}}\]

C)
\[{{\tan }^{-1}}\frac{3a+{{a}^{3}}}{1-3{{a}^{2}}}\]

D)
\[{{\tan }^{-1}}\frac{3a-{{a}^{3}}}{1-3{{a}^{2}}}\]
View Solution
125)

\[4{{\tan }^{-1}}\frac{1}{5}-{{\tan }^{-1}}\frac{1}{239}\]is equal to [MNR 1995]

A)
\[\pi \]

B)
\[\frac{\pi }{2}\]

C)
\[\frac{\pi }{3}\]

D)
\[\frac{\pi }{4}\]
View Solution
126)

If \[3{{\sin }^{-1}}\frac{2x}{1-{{x}^{2}}}-4{{\cos }^{-1}}\frac{1-{{x}^{2}}}{1+{{x}^{2}}}+2{{\tan }^{-1}}\frac{2x}{1-{{x}^{2}}}=\frac{\pi }{3}\] then \[x\] =

A)
\[\sqrt{3}\]

B)
\[\frac{1}{\sqrt{3}}\]

C)
1

D)
None of these
View Solution
127)

The value of \[\sin \left( 2{{\tan }^{-1}}\left( \frac{1}{3} \right) \right)+\cos ({{\tan }^{-1}}2\sqrt{2})=\] [AMU 1999]

A)
\[\frac{16}{15}\]

B)
\[\frac{14}{15}\]

C)
\[\frac{12}{15}\]

D)
\[\frac{11}{15}\]
View Solution
128)

\[\sin \left( \frac{1}{2}{{\cos }^{-1}}\frac{4}{5} \right)=\] [Karnataka CET 2003]

A)
\[\frac{1}{\sqrt{10}}\]

B)
\[-\frac{1}{\sqrt{10}}\]

C)
\[\frac{1}{10}\].

D)
\[-\frac{1}{10}\]
View Solution
129)

The value of \[{{\cos }^{-1}}(\cos 12)-{{\sin }^{-1}}(\sin 14)\] is [J & K 2005]

A)
- 2

B)
\[8\pi -26\]

C)
\[4\pi +2\]

D)
None of these
View Solution
130)

\[{{\cos }^{-1}}\left( \frac{3+5\cos x}{5+3\cos x} \right)\] is equal to [Kerala (Engg.) 2005]

A)
\[{{\tan }^{-1}}\left( \frac{1}{2}\tan \frac{x}{2} \right)\]

B)
\[2{{\tan }^{-1}}\left( 2\tan \frac{x}{2} \right)\]

C)
\[\frac{1}{2}{{\tan }^{-1}}\left( 2\tan \frac{x}{2} \right)\]

D)
\[2{{\tan }^{-1}}\left( \frac{1}{2}\tan \frac{x}{2} \right)\]

E)
\[{{\tan }^{-1}}\left( \tan \frac{x}{2} \right)\]
View Solution
131)

If \[{{\cos }^{-1}}x-{{\cos }^{-1}}\frac{y}{2}=\alpha \], then \[4{{x}^{2}}-4xy\cos \alpha +{{y}^{2}}\] is equal to [AIEEE 2005]

A)
\[4{{\sin }^{2}}\alpha \]

B)
\[-4{{\sin }^{2}}\alpha \]

C)
\[2\sin 2\alpha \]

D)
\[4\]
View Solution
132)

If \[{{\tan }^{-1}}x+{{\tan }^{-1}}y=\frac{\pi }{4}\] then [Karnataka CET 2005]

A)
\[x+y+xy=1\]

B)
\[x+y-xy=1\]

C)
\[x+y+xy+1=0\]

D)
\[x+y-xy+1=0\]
View Solution
133)

If \[{{\sin }^{-1}}(1-x)-2{{\sin }^{-1}}x=\pi /2\], then x equals [Orissa JEE 2005]

A)
\[\left( 0,\,-\frac{1}{2} \right)\]

B)
\[\left( \frac{1}{2},\,0 \right)\]

C)
{0}

D)
(-1, 0)
View Solution
134)

If \[\angle A={{90}^{o}}\] in the triangle ABC, then \[{{\tan }^{-1}}\left( \frac{c}{a+b} \right)+{{\tan }^{-1}}\left( \frac{b}{a+c} \right)=\] [Kerala (Engg.) 2005]

A)
0

B)
1

C)
\[\pi /4\]

D)
\[\pi /6\]

E)
\[\pi /8\]
View Solution
135)

The solution of \[{{\sin }^{-1}}x-{{\sin }^{-1}}2x=\pm \frac{\pi }{3}\] is [Karnataka CET 2005]

A)
\[\pm \frac{1}{3}\]

B)
\[\pm \frac{1}{4}\]

C)
\[\pm \frac{\sqrt{3}}{2}\]

D)
\[\pm \frac{1}{2}\]
View Solution
136)

For the equation \[{{\cos }^{-1}}x+{{\cos }^{-1}}2x+\pi =0\], the number of real solution is [Orissa JEE 2005]

A)
1

B)
2

C)
0

D)
\[\infty \]
View Solution
137)

\[\sin \text{ }\left[ 3\,{{\sin }^{-1}}\left( \frac{1}{5} \right) \right]=\] [Kerala (Engg.) 2005]

A)
71/125

B)
74/125

C)
3/5

D)
1/2

E)
- 3/5
View Solution

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JEE Main & Advanced Mathematics Inverse Trigonometric Functions Question Bank

done Inverse trigonometric functions Total Questions - 137

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Inverse trigonometric functions Total Questions - 137