# 10th Class Mathematics Introduction to Trigonometry Question Bank

### done Trigonometry

• A) $\frac{\pi }{2}$

B) $\frac{2pi }{5}$

C) $\frac{\pi }{5}$

D) $3\pi$

• A) ${{\sec }^{2}}\alpha =1-{{\tan }^{2}}\alpha$

B) ${{\sin }^{2}}\alpha =1+{{\cos }^{2}}\alpha$

C) $\tan \,\alpha \,\,\cot =1$

D) None of these

• A) $\sin (90{}^\circ -\theta )=sin\theta$

B) $cos(90{}^\circ -\theta )=\cos \theta$

C) $\sin (90{}^\circ -\theta )=\cos \theta$

D) $tan(90{}^\circ +\theta )=\tan \theta$

• A) 0

B) 1

C) $\text{sinB}\,\,\text{cos}\,\text{B}$

D) $2\,\,{{\sin }^{2}}B$

• A) 1

B) 2

C) 3

D) $\sqrt{2}$

• A) $\frac{\sqrt{2}}{3}$

B) $\frac{2\sqrt{2}}{3}$

C) $\frac{2}{3}$

D) $\frac{3}{4}$

• A) $\frac{1}{3}$

B) $\frac{1}{6}$

C) $\frac{4}{5}$

D) $\frac{3}{2}$

• A) 3

B) 2

C) $\frac{3}{2}$

D) 1

•  Assertion (A):$\frac{1}{1+{{\sin }^{2}}x}-\frac{1}{1+{{\sec }^{2}}x}\ne \frac{1}{1+{{\cos }^{2}}x}-\frac{1}{1+\text{cose}{{\text{c}}^{2}}x}$ Reason (R): $\sin x\ne \cos x$
Of these statements:

A)  Both A and II are true and R is the correct explanation of A

B)  Both A and R are true, but R is not the correct explanation of A.

C)  A is true, but R is false.

D)  A is false, but R is true.

• A) 1

B) 2

C) $\frac{1}{\sqrt{2}}$

D) $2\sqrt{2}$

•  I. $\text{cosec}\theta -\text{cot}\theta$ II. $\frac{1}{\text{cosec}\theta +\text{cot}\theta }$

A) both I and II are correct

B) both are wrong

C) I is wrong, II is correct

D) I is correct, I is wrong

• A) $\frac{1}{\sqrt{6}}$

B) $\frac{\sqrt{5}}{\sqrt{6}}$

C) $-\frac{1}{\sqrt{6}}$

D) $-\frac{\sqrt{5}}{\sqrt{6}}$

• A) 1

B) 2

C) -1

D) 0

• A) $\frac{1}{\sqrt{2}}$

B) $2$

C) $cos\,5{}^\circ$

D) $\sin \,5{}^\circ$

• A) $1+\frac{1}{\sqrt{3}}$

B) $2-\sqrt{3}$

C) $2+\sqrt{3}$

D) $1+\sqrt{3}$

• A) ${{\sin }^{2}}A-{{\sin }^{2}}B$

B) ${{\cos }^{2}}A-{{\sin }^{2}}B$

C) ${{\cos }^{2}}A-{{\cos }^{2}}B$

D) $\cos 2A\,\,.\,\,\cos 2B$

• A) $\sin 2A$

B) $-\sin 2A$

C) $\cos \,2A$

D) $-\cos \,2A$

• A) $\sqrt{2}\cos \,\theta$

B) $\sqrt{2}sin\,\theta$

C) $0$

D) $1$

• A) $(1-k)$

B) $(1+k)$

C) $\frac{1}{k}$

D) $1-\frac{1}{k}$

• A) 1

B) 2

C) 3

D) 4

• A) $2x$

B) $\frac{x}{2}$

C) $3x$

D) $\frac{x}{3}$

• A) $30{}^\circ$

B) $45{}^\circ$

C) $60{}^\circ$

D) None of these

• A) $\frac{AB}{BC}$

B) $\frac{BC}{AB}$

C) $\frac{BC}{CD}$

D) $\frac{CD}{BC}$

• A) $2\tan A\,\,\tan B\,\,\tan C$

B) $\tan A\,\,\tan B\,\,\tan C$

C) $\cot A\,\,\cot B\,\,\cot C$

D) $\tan A\,\,\tan B\,\,\cot C$

• A) $\text{cosec}\,A+\cot A$

B) $\text{cosec}\,A-\cot A$

C) $\text{sec}\,A+tanA$

D) $\text{sec}\,A-tanA$

• A) $30{}^\circ$

B) $75{}^\circ$

C) $60{}^\circ$

D) $45{}^\circ$

• A) $\frac{1}{\sqrt{3}}\,\,meter$

B) $\frac{1}{3}\,\,meter$

C) $\sqrt{3}\,\,meter$

D) $3\,\,meter$

• A) $9$

B) $\frac{9}{5}$

C) $\frac{1}{3}$

D) $\frac{1}{9}$

• A) $2\frac{7}{12}$

B) $1\frac{5}{12}$

C) $-2\frac{5}{12}$

D) $-1\frac{5}{12}$

• A) sin B = 2 sin E

B) sin E = 2 sin B

C) sin B = sin E

D) sin A = sin D

• A) $2a=b$

B) $3a=2b$

C) $a=b$

D) $a=2b$

• A) $(3+\sqrt{3})\,km$

B) $(3-\sqrt{3})\,km$

C) $2\sqrt{3}\,km$

D) $3\sqrt{3}\,km$

• A) $r\,\text{cosec}\frac{\alpha }{2}\sin \beta$

B) $\frac{r\,\text{cosec}\,\alpha }{2\sin \beta }$

C) $\frac{r\,\text{cosec}\,\alpha }{2\cos \beta }$

D) $r\sin \alpha \sin \beta$

• A) $\frac{5}{12}$

B) $\frac{12}{13}$

C) $\frac{5}{13}$

D) $\frac{13}{12}$

• A) 10 m

B) 15 m

C) $15\sqrt{3}\,\,m$

D) 30 m

• A) 1

B) $\frac{1}{2}$

C) $\frac{1}{4}$

D) 2

• A) $30{}^\circ$

B) $45{}^\circ$

C) $60{}^\circ$

D) $90{}^\circ$

• A) 1

B) 0

C) $\frac{1}{2}$

D) 2

• A) ${{\cos }^{4}}\theta -{{\sin }^{4}}\theta ={{\cos }^{2}}\theta -{{\sin }^{2}}\theta$

B) $1{{\tan }^{2}}\theta ={{\sec }^{2}}\theta$

C) $\sin 40{}^\circ +\cos 50{}^\circ =2\sin 40{}^\circ$

D) ${{\sin }^{2}}\theta +{{\cos }^{2}}\theta =2$

• A) $0$

B) $\frac{1}{2}$

C) $1$

D) $-\frac{1}{2}$

• A) 0

B) 1

C) 2

D) 3

• A) greater than 1

B) less than 1

C) greater than or equal to 2

D) equal to 2

• A) $x+y=z$

B) $xy=z$

C) $xz=y$

D) $y+z=x$

• A) 2

B) 3

C) 1

D) 0

• A) always negative

B) always positive

C) sometimes positive and sometimes negative

D) zero

• A) ${{\cos }^{2}}A$

B) $se{{c}^{2}}A$

C) $ta{{n}^{2}}A$

D) $\text{cose}{{\text{c}}^{2}}A$

• A) $30{}^\circ$

B) $45{}^\circ$

C) $60{}^\circ$

D) $75{}^\circ$

• A) $0$

B) $1$

C) $\frac{1}{2}$

D) $\frac{\sqrt{3}}{2}$

• A) $\frac{13}{6}$

B) $\frac{1}1{6}$

C) $\frac{7}{6}$

D) $\frac{5}{6}$

• A) 0

B) $\frac{1}{2}$

C) $\frac{3}{4}$

D) 1

• A) $\frac{49}{12}$

B) $\frac{7}{3}$

C) $\frac{14}{9}$

D) $\frac{4}{3}$

• A) $\frac{1}{3}$

B) $\frac{2}{3}$

C) $\frac{4}{3}$

D) $\frac{5}{3}$

• A) $\sin 45{}^\circ \cos 45{}^\circ =1$

B) ${{\sin }^{2}}45{}^\circ -{{\cos }^{2}}45{}^\circ =1$

C) $\sin 30{}^\circ +\cos 60{}^\circ =1$

D) $co{{s}^{2}}30{}^\circ -\cos 60{}^\circ =1$

• A) $2\sin \theta \,\,.\,\,\cos \theta$

B) $\operatorname{cosec}\theta \,\,.\,\,sec\theta$

C) $\sin \,\theta \,\,.\,\,cos\theta$

D) $2cosec\,\theta \,\,.\,\,sin\theta$

• A) $\theta =\frac{\pi }{2}$

B) $\theta =\frac{\pi }{3}$

C) $\theta =\frac{\pi }{4}$

D) $\theta =\frac{\pi }{6}$

• A)  decreases

B)  increases

C)  neither increases or decreases

D)  none of these

• A) $0$

B) $1$

C) $-\frac{1}{4}$

D) $-2$

• A) $0$

B) $2\sqrt{2}$

C) $\sqrt{2}$

D) $1$

• A) $\frac{\sin C}{\sin B}$

B) $\frac{\cos B}{\cos C}$

C) $\frac{\sin B}{\sin C}$

D) $\frac{tanB}{tanC}$

• A) $\operatorname{cosec}\,\theta$

B) $2\operatorname{cosec}\,\theta$

C) $sec\,\theta$

D) $2sec\,\theta$

• A) $\frac{1+\cos \theta }{1-\cos \theta }$

B) $\frac{1+sin\theta }{1-sin\theta }$

C) $\frac{1-\cos \theta }{1+\cos \theta }$

D) $\frac{1-sin\theta }{1+sin\theta }$

• A) ${{\sec }^{2}}\theta \,\,.\,\,\,{{\cot }^{2}}\theta$

B) ${{\sec }^{2}}\theta \,\,.\,\,\,ta{{n}^{2}}\theta$

C) $cose{{c}^{2}}\theta \,\,.\,\,\,{{\cot }^{2}}\theta$

D) $se{{c}^{2}}\theta \,\,.\,\,\,{{\operatorname{cosec}}^{2}}\theta$

• A) 10

B) 11

C) 12

D) 13

• A) $1-n$

B) $1+n$

C) $1-{{n}^{2}}$

D) $1+{{n}^{2}}$

• A) 4.5

B) 4

C) 8

D) 9

• A) 1

B) 2

C) 3

D) None of these

• A) 5

B) 1

C) 2

D) 3

• A) 0

B) -1

C) 1

D) 2

• A) $\frac{1-{{p}^{2}}}{2(1+{{p}^{2}})}$

B) $\frac{1+{{p}^{2}}}{2(1-{{p}^{2}})}$

C) $\frac{1-2p}{1+{{p}^{2}}}$

D) $\frac{1-{{p}^{2}}}{1+{{p}^{2}}}$

• A) $\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1$

B) $\frac{{{a}^{2}}}{{{x}^{2}}}+\frac{{{b}^{2}}}{{{y}^{2}}}=1$

C) $\frac{{{a}^{2}}}{{{x}^{2}}}-\frac{{{b}^{2}}}{{{y}^{2}}}=1$

D) $\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1$

• A) 1

B) 2

C) 3

D) 4

• A) $30{}^\circ$

B) $45{}^\circ$

C) $60{}^\circ$

D) None of these

• A) $30{}^\circ$

B) $45{}^\circ$

C) $60{}^\circ$

D) $90{}^\circ$

• A) 1

B) .766

C) $\frac{1}{766}$

D) 0

• A) ${{\sin }^{2}}\theta$

B) $1$

C) ${{\cos }^{2}}\theta$

D) $0$

• A) $\frac{1}{2}$

B) $0$

C) $1$

D) $\sqrt{3}$

• A) $0$

B) $-1$

C) $-\frac{1}{2}$

D) $\frac{1}{2}$

• A) $\sin 2x[\tan x+\cot x]=2$

B) $1-cos2x=2co{{s}^{2}}x$

C) $ta{{n}^{2}}x+{{\cot }^{2}}x={{\sec }^{2}}x+{{\operatorname{cosec}}^{2}}x$

D) ${{\cot }^{2}}x-{{\tan }^{2}}x=1$

• A) $\frac{88}{160}$

B)   $\frac{91}{160}$

C)   $\frac{92}{160}$

D)   $\frac{93}{160}$

• A) 2

B) 1

C) 4

D) 3

• A) $\frac{1+\cos \theta }{\sin \theta }$

B) $\frac{1+\sin \theta }{\sin \theta }$

C) $\frac{1-\cos \theta }{\sin \theta }$

D) $\frac{1-sin\theta }{\sin \theta }$

• A) $45{}^\circ$

B) $60{}^\circ$

C) $105{}^\circ$

D) $150{}^\circ$

• A) $\frac{32}{\sqrt{3}}(\sqrt{3}+1)\,\,meters$

B) $32(\sqrt{3}+1)\,\,meters$

C) $32\sqrt{3}\,\,meters$

D) $\frac{32}{3}(\sqrt{3}+1)\,\,meters$

• A) $\frac{200(\sqrt{3}-1)}{(\sqrt{3}+1)}\,\,meters$

B) $\frac{200(\sqrt{3}-1)}{\sqrt{3}}\,\,meters$

C) $\frac{200(\sqrt{3}+1)}{\sqrt{3}}\,\,meters$

D)   $\frac{200(\sqrt{3}+1)}{(\sqrt{3}-1)}\,\,meters$

• A) $250\sqrt{3}\,\,meters$

B) $\frac{500}{\sqrt{3}}\,\,meters$

C) $500\sqrt{3}\,\,meters$

D) $250\,\,meters$

• A) $\frac{a}{b}$

B) $\sqrt{\frac{a}{b}}$

C) $ab$

D) $\sqrt{ab}$

• A) $\frac{\sqrt{3}-1}{2\sqrt{2}}$

B) $\frac{\sqrt{3}-1}{\sqrt{2}}$

C) $\frac{\sqrt{3}+1}{2\sqrt{2}}$

D) $\frac{\sqrt{3}+1}{\sqrt{2}}$

• A) $less\text{ }than\,\,\frac{\pi }{4}$

B) $equal\text{ }to\,\,\frac{\pi }{4}$

C) $between\,\,\frac{\pi }{4}\,\,and\,\,\frac{\pi }{3}$

D) $greater\text{ }than\,\,\frac{\pi }{3}$

• A) $2+\sqrt{3}$

B) $2-\sqrt{3}$

C) $3+\sqrt{3}$

D) $3-\sqrt{3}$

• A) $h(\cot \,y+\cot \,x)$

B) $h(tan\,x+tan\,y)$

C) $h(1+tan\,x\cot \,y)$

D) $h(tan\,y\cot \,x+1)$

• A) 5 m

B) 7.5 m

C) 10 m

D) 12.5 m

• A) $\frac{\sqrt{3}+2}{4}$

B) $\frac{\sqrt{3}+2}{2}$

C) $\frac{\sqrt{3}-2}{4}$

D) $\frac{\sqrt{3}-2}{2}$

• A) $\frac{5}{34}$

B) $\frac{5}{16}$

C) $\frac{5}{-34}$

D) $\frac{-5}{16}$

• A) $\sqrt{3}$

B) $1$

C) $\frac{1}{\sqrt{3}}$

D) not defined

• A) $\frac{27}{16}$

B) $\frac{7}{16}$

C) $\frac{5}{16}$

D) $\frac{3}{16}$

• A) $\cos (A+B)=cosA+\operatorname{cosB}$

B) $\cos (A+B)=cosA\operatorname{cosB}$

C) $\cos (A+B)=cosA\operatorname{cosB}-\sin A\sin B$

D) $\cos (A+B)=cosA\operatorname{cosB}+\sin A\sin B$

• A) 45

B) 30

C) 50

D) 80

• A) $3\sqrt{3}$

B) $2\sqrt{3}$

C) $\sqrt{3}$

D) $6\sqrt{3}$

• A) 0.6293

B) 0.6307

C) 0.6361

D) 0.6414

• A) $\tan \,C$

B) $c$

C) $\frac{c}{ab}$

D) $\frac{{{c}^{2}}}{ab}$

• A) ${{\cos }^{2}}\theta -{{\sin }^{2}}\theta =1$

B) ${{\operatorname{cosec}}^{2}}\theta -{{\sec }^{2}}\theta =1$

C) ${{\cot }^{2}}\theta -{{\tan }^{2}}\theta =1$

D) $se{{c}^{2}}\theta -{{\tan }^{2}}\theta =1$

• A) $m+n$

B) $m\,n$

C) $\sqrt{m\,n}$

D) ${{m}^{2}}+{{n}^{2}}$

• A) $ta{{n}^{4}}\theta -{{\tan }^{2}}\theta$

B) $ta{{n}^{2}}\theta -{{\tan }^{4}}\theta$

C) $ta{{n}^{2}}\theta +{{\tan }^{4}}\theta$

D) $2ta{{n}^{2}}\theta$

• A) $-\frac{1}{2}$

B) $-\frac{1}{4}$

C) $\frac{1}{4}$

D) $\frac{1}{2}$

• A) $\frac{1}{\sqrt{3}}$

B) $1$

C) $\sqrt{3}$

D) $\infty$

• A) $\frac{1}{16}$

B) $\frac{1}{8}$

C) $\frac{5}{16}$

D) $\frac{3}{16}$

• A) $\frac{1}{5}$

B) $\frac{9}{5}$

C) $\frac{12}{25}$

D) $\frac{25}{12}$

• A) $\cot \theta (1-ta{{n}^{2}}\theta )$

B) $\cot \theta (ta{{n}^{2}}\theta -1)$

C) $\cot \theta ta{{n}^{2}}\theta$

D) $tan\theta {{\operatorname{cosec}}^{2}}\theta$

• A) $si{{n}^{2}}\theta +{{\cos }^{2}}\theta$

B) $si{{n}^{3}}\theta -{{\cos }^{3}}\theta$

C) $si{{n}^{4}}\theta +{{\cos }^{4}}\theta$

D) $si{{n}^{2}}\theta -{{\cos }^{2}}\theta$

• A) ${{\left( \frac{1+{{\tan }^{2}}\theta }{1+{{\cot }^{2}}\theta } \right)}^{2}}$

B) ${{\left( \frac{1+{{\cot }^{2}}\theta }{1+ta{{n}^{2}}\theta } \right)}^{2}}$

C) ${{\left( \frac{1+\tan \theta }{1-\cot \theta } \right)}^{2}}$

D) ${{\left( \frac{1-{{\cot }^{2}}\theta }{1+ta{{n}^{2}}\theta } \right)}^{2}}$

• A) $\left( \frac{1-cos\theta }{1+\cos \theta } \right)$

B) $\left( \frac{1+cos\theta }{1-\cos \theta } \right)$

C) $\left( \frac{cos\theta -1}{\cos \theta +1} \right)$

D) $\left( \frac{cos\theta +1}{\cos \theta -1} \right)$

• A) $1$

B) ${{\cos }^{2}}\theta$

C) $\cot \theta$

D) $tan\theta$

• A) ${{\sin }^{2}}\theta -{{\cos }^{2}}\theta =1$

B) $cose{{c}^{2}}\theta -{{\cot }^{2}}\theta =1$

C) $cose{{c}^{2}}\theta -{{\cos }^{2}}\theta =1$

D)   $se{{c}^{2}}\theta -si{{n}^{2}}\theta =1$

• A)  increases

B) decreases

C) remains constant

D) increases, then decreases

• A) $\sin \theta =1-\cos \theta$

B) $sec\theta -\tan \theta =\frac{1}{\sec \theta +\tan \theta }$

C) ${{\tan }^{2}}\theta -{{\sin }^{2}}\theta ={{\tan }^{2}}\theta {{\sin }^{2}}\theta$

D) $\sin \frac{\pi }{3}=\cos \frac{\pi }{6}$

• A) $3-{{\cot }^{2}}\theta$

B) $3+{{\cot }^{2}}\theta$

C) $3-ta{{n}^{2}}\theta$

D) $3+ta{{n}^{2}}\theta$

• A) 1

B) 1.5

C) 2

D) 2.5

• A) $0$

B) $1$

C) $\tan \theta$

D) $cot\theta$

• A) $20\text{ }meters$

B) $10\sqrt{3}\text{ }meters$

C) $10\text{ }meters$

D) $10\sqrt{2}\text{ }meters$

• A) $50\sqrt{3}\text{ }meters$

B) $\frac{50}{\sqrt{3}}\text{ }meters$

C) $100\sqrt{3}\text{ }meters$

D)   $\frac{100}{\sqrt{3}}\text{ }meters$

• A) $50\sqrt{3}\,\,m$

B) $50(\sqrt{3}+1)\,\,m$

C) $50(\sqrt{3}-1)\,\,m$

D) $5\left( 1-\frac{1}{\sqrt{3}} \right)\,\,m$

• A) 50 metres

B) 75 metres

C) 100 metres

D) 150 metres

• A) $\frac{d\tan x\tan y}{\tan y-\tan x}$

B) $d(\tan y+\tan x)$

C) $d(\tan y-\tan x)$

D) $\frac{d\tan x\tan y}{\tan y+\tan x}$

• A) $\frac{h}{\sqrt{3}}$

B) $h$

C) $\sqrt{2}h$

D) $2h$

• A) $30{}^\circ$

B) $45{}^\circ$

C) $60{}^\circ$

D) $90{}^\circ$

• A) $\frac{1}{4}$

B) $\frac{3}{4}$

C) $\frac{3}{5}$

D) $\frac{5}{3}$

• A) $\frac{1}{\sqrt{6}}$

B) $-\frac{1}{\sqrt{6}}$

C) $-\sqrt{\frac{5}{6}}$

D) $\frac{\sqrt{5}}{\sqrt{6}}$

• A) -4

B) -2

C) 2

D) 4

• A) $x-y$

B) $x+y$

C) $\frac{1}{x}-\frac{1}{y}$

D) $\frac{1}{x}+\frac{1}{y}$

• A) $\frac{(sinA+sinB)}{(sinA-sinB)}=\frac{\tan \frac{A+B}{2}}{\tan \frac{A-B}{2}}$

B) ${{\sin }^{2}}A-{{\cos }^{2}}B=\sin (A+B)sin(A-B)$

C) $cosA-\cos B=2\cos \frac{A+B}{2}coss\frac{B-A}{2}$

D)   $co{{s}^{2}}A-{{\cos }^{2}}B=\sin (A+B)sin(B-A)$

• A) $0$

B) ${{\sin }^{2}}\theta$

C) $co{{s}^{2}}\theta$

D) $1$

• A) $12\,\,c{{m}^{2}}$

B) $6\sqrt{2}\,c{{m}^{2}}$

C) $\frac{12}{\sqrt{3}}\,c{{m}^{2}}$

D) $6\,\,c{{m}^{2}}$

• A) -2

B) -1

C) 0

D) 1

• A)   $\frac{1}{2}$

B) $\frac{3}{2}$

C) $\frac{5}{2}$

D)   $\frac{7}{2}$

• A) $\frac{30}{\sqrt{3}}m$

B)   $\frac{30\sqrt{3}}{2}m$

C) $30\,\,m$

D) $30\sqrt{3}\,\,m$

• A) 0

B) 2

C) -3

D) -5

• A) $\alpha =\frac{\pi }{2}$

B) $\alpha =\frac{\pi }{3}$

C) $\alpha =\frac{\pi }{4}$

D) $\alpha =\frac{\pi }{6}$

• A) $30{}^\circ$

B) $60{}^\circ$

C) $120{}^\circ$

D) $240{}^\circ$

• A) 10

B) 15

C) 20

D) 22

• A) $\frac{5}{2}\,m$

B) $\frac{5}{\sqrt{2}}\,m$

C) $5\sqrt{2}\,m$

D) $5\,m$

• A) 125 m

B) 120 m

C) 115m

D) 100 m

• A) $\sqrt{2}\sin \theta$

B) $\sqrt{2}co{{s}^{2}}\theta$

C) $\sqrt{2}cos\theta$

D) $\sqrt{2}si{{n}^{2}}\theta$

• A) always negative

B) always positive

C) sometimes positive, sometimes negative

D) 0

• A) $0{}^\circ$

B) $30{}^\circ$

C) $45{}^\circ$

D)  $60{}^\circ$

• A)   $\frac{\sqrt{3}+1}{2}$

B) $\frac{\sqrt{3}+1}{2\sqrt{2}}$

C)   $\frac{-(\sqrt{3}+1)}{2\sqrt{2}}$

D)   $\frac{\sqrt{3}-1}{2\sqrt{2}}$

• A) ${{\cos }^{4}}\theta -{{\sin }^{4}}\theta ={{\cos }^{2}}\theta -{{\sin }^{2}}\theta$

B) $1+{{\tan }^{2}}\theta ={{\operatorname{csec}}^{2}}\theta$

C) $\sin 40{}^\circ +\cos 50{}^\circ =2\sin 40{}^\circ$

D) ${{\sin }^{2}}\theta +{{\cos }^{2}}(-\theta )=-1$

• A) -1

B) 2

C) 0

D) 2 sin 2A

• A) $4\cos \theta \,\cos 2\theta$

B) $4\sin \theta \,\cos 2\theta$

C) $4\sin \theta \,\sin 2\theta$

D) $4\cos \theta \,\sin 2\theta$

• A) $\frac{13}{16}$

B) $5$

C) $1$

D) $-\frac{1}{2}$

• A) $1$

B) $-1$

C) $\frac{1}{2}$

D) $0$

• A) 1

B) - 1

C) 0

D) $\frac{1}{2}$

• A) $0{}^\circ$

B) $\frac{\pi }{4}$

C) $\frac{\pi }{6}$

D) $\frac{\pi }{2}$

• A) $\frac{3}{160}$

B) $\frac{841}{160}$

C) $\frac{41}{160}$

D) $\frac{31}{160}$

• A) $\frac{59}{41}$

B) $\frac{35}{41}$

C) $\frac{41}{59}$

D) $\frac{41}{35}$

• A) $0$

B) $2\sqrt{2}$

C) $-2\sqrt{2}$

D) $1$

• A) 2

B) -2

C) 1

D) 0

• A) 0

B) -1

C) 1

D) 2

• A) 0

B) 1

C) 2

D) -2

• A) $\frac{\sqrt{5}-1}{4}$

B) $\frac{\sqrt{5}+1}{4}$

C) $-\frac{\sqrt{5}+1}{4}$

D) $\frac{1-\sqrt{5}}{4}$

• A) 4

B) 6

C) -2

D) 0

• A) $\frac{\sqrt{3}+1}{2\sqrt{2}}$

B) $\frac{\sqrt{3}-1}{2\sqrt{2}}$

C) $\frac{1-\sqrt{3}}{2\sqrt{2}}$

D) $\frac{\sqrt{3}+1}{2+\sqrt{2}}$

• A) $\sin (A+C)=0$

B) $\sin (A+B)=0$

C) $cos(B+D)=-1$

D) $sin(A+B+\text{C}+D)=0$

• A) 0

B) 1

C)  infinity

D) none

• A) -1

B) 0

C) 1

D) 2

• A) $0$

B) $\frac{1}{2}$

C) $1$

D) $-\frac{1}{2}$

• A) 1

B) 2

C) 6

D) 7

• A) $\sec \alpha \,\cdot \,\operatorname{cosec}\alpha$

B) $\sin \alpha \,\cdot \,\cos \alpha$

C) $\sec \alpha \,\cdot \,\operatorname{cosec}\alpha +1$

D) $\sin \alpha \,\cdot \,\cos \alpha +1$

• A) 0

B) 1

C) $\infty$

D) -1

• A) $1$

B) $0$

C) $\tan A\,\,\tan B\,\,\tan C$

D) $-1$

• A) 1

B) 2

C) 0

D) -1

• A) 0

B) -1

C) 1

D) Cannot be found

• A) $\frac{2x}{1-{{x}^{2}}}$

B) $\frac{1-{{x}^{2}}}{2x}$

C) $\frac{1}{1+{{x}^{2}}}$

D) $\frac{1}{1-{{x}^{2}}}$

• A) 0

B) 1

C) $\frac{50}{37}$

D) $\frac{37}{2}$

• A)  $a\,or\,\frac{1}{a}$

B) $2a\,or\,\frac{1}{2a}$

C)  $4a\,\,or\,\frac{1}{4a}$

D) 1

• A) $63{}^\circ$

B) $35{}^\circ$

C) $27{}^\circ$

D) $54{}^\circ$

• A) $\frac{\pi }{6}$

B) $\frac{\pi }{4}$

C) $\frac{\pi }{3}$

D) $\frac{\pi }{5}$

• A) 0

B) - 1

C) 1

D) 2

• A)  1

B) $\pm \sqrt{5}$

C)  $\frac{1}{2}$

D) $\pm \sqrt{3}$

• A) $\frac{1}{2\sqrt{2}}(\sqrt{3}+1)$

B) $\frac{1}{2}(\sqrt{3}-1)$

C) $\frac{\sqrt{3}}{2}$

D) $\frac{1}{2}$

• A) $\frac{\sqrt{3}+1}{2}$

B) $\sqrt{3}$

C) $\frac{1}{2}$

D) 1

• A) $\text{2}\left( \text{1}+\text{cosA} \right)\left( \text{1}-\text{cosA} \right)$

B) $\text{2}\left( \text{l}-\text{sinA} \right)\left( \text{l}+\text{cosA} \right)$

C) $\text{2}\left( \text{l}+\text{sinA} \right)\left( \text{l}-\text{sin A} \right)$

D) $\text{2}\left( \text{l}+\text{sinA} \right)\left( \text{l}-\text{cosA} \right)$

• A) 3

B) 2

C) 1

D) 0

• A) $\text{sinA}-\text{cosA}$

B) sin A + cos A

C) $\text{1 }-\text{ cos A}$

D) $\text{1}-\text{ sin A}$

• A) $\frac{\cos A}{1+\sin A}$

B) $\frac{\sin A}{1-\cos A}$

C) $\frac{\tan A}{1+\tan A}$

D) $\frac{\tan A}{1+\cos A}$

• A)  $-\frac{1}{5}$

B)  $\frac{1}{5}$

C)  $-5$

D) 5

• A) $30{}^\circ ,\text{ }60{}^\circ$

B) $30{}^\circ ,\text{ }120{}^\circ$

C) $60{}^\circ ,\text{ }120{}^\circ$

D) $90{}^\circ ,\text{ }120{}^\circ$

• A)  $40\sqrt{3}m$

B) $\frac{40\sqrt{3}}{3}m$

C) $20 m$

D) $\frac{40\sqrt{3}}{2}m$

• A)  $-\frac{4}{3}$

B) $-\frac{3}{4}$

C) $-\frac{2}{3}$

D) $-\frac{1}{3}$

• A) 0

B) 2

C) 1

D) $\frac{1}{2}$

• A) $\frac{\sqrt{3}}{2}$

B) $-\frac{1}{2}$

C) $\frac{1}{\sqrt{2}}$

D) $\frac{1}{2}$

• A) 25

B) 50

C) 75

D) 80

• A) $3\sqrt{3}\,m$

B) $\sqrt{7}\,m$

C) $2\sqrt{3}\,m$

D) $\frac{1}{\sqrt{3}}\,m$

• A) ${{\cos }^{-1}}\left( \frac{1}{3} \right)$

B) ${{\cos }^{-1}}\left( \frac{1}{6} \right)$

C) ${{\sin }^{-1}}\left( \frac{1}{6} \right)$

D) ${{\sin }^{-1}}\left( \frac{1}{3} \right)$

• A) $\frac{\sqrt{3}}{2}$

B) $\sqrt{3}+1$

C) $\sqrt{3}-1$

D) $\frac{2}{\sqrt{3}}$

• A) 1

B) 2

C) 3

D) 4

• A) 3

B) 2

C) 1

D) None of these

• A) $\text{sec }\theta$

B) $\text{cosec }\theta$

C) $\text{tan }\theta$

D) 1

• A)  $\frac{1}{2}$

B)  $-\frac{\sqrt{3}}{2}$

C)  $\frac{\sqrt{3}}{2}$

D)         $\frac{1}{\sqrt{2}}$

• A) $50\sqrt{3}$metres

B) $\frac{20}{\sqrt{3}}$ metres

C) $-50$metres

D) 50 metres

• A) $\frac{\sqrt{3}}{2}$

B) $\sqrt{3}-1$

C)   $\frac{1}{2}$

D) $\sqrt{2}-1$

• A) 0

B) 1

C) ${{\sin }^{2}}\theta$

D) $\cos e{{c}^{2}}\theta$

• A) $\frac{1}{2}$

B) $\frac{1}{4}$

C) $\frac{1}{8}$

D) $\frac{1}{16}$

• A) 10 mts

B) 15 mts

C) 20 mts

D) $10\sqrt{3}$ mts

• A) 0

B) 1

C) 2

D) -2

• A) $0{}^\circ$

B) $45{}^\circ$

C) $60{}^\circ$

D) $90{}^\circ$

• A) $\frac{1}{2}$

B) 0

C) 1

D) 2