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question_answer1)
If \[\theta \]is eliminated from the equations \[x=a\,\cos (\theta -\alpha )\]and \[y=b\,\cos (\theta -\beta )\], then \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}-\frac{2xy}{ab}\cos (\alpha -\beta )\]is equal to
A)
\[{{\sec }^{2}}(\alpha -\beta )\] done
clear
B)
\[\cos e{{c}^{2}}(\alpha -\beta )\] done
clear
C)
\[{{\cos }^{2}}(-\beta )\] done
clear
D)
\[si{{n}^{2}}(\alpha -\beta )\] done
clear
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question_answer2)
If \[\sin (y+z-x)\],\[\sin (z+x-y)\], \[\sin (x+y-z)\]are in A.P., then \[\tan x,\tan y,\tan z\]are in
A)
A.P. done
clear
B)
G.P. done
clear
C)
H.P. done
clear
D)
None of these done
clear
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question_answer3)
If \[{{\tan }^{2}}\frac{\pi -A}{4}+{{\tan }^{2}}\frac{\pi -B}{4}+{{\tan }^{2}}\frac{\pi -C}{4}=1,then\text{ }\Delta ABC\,\,is\]
A)
equilateral done
clear
B)
isosceles done
clear
C)
scalene done
clear
D)
none of these done
clear
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question_answer4)
If A, B, C are angles of a triangle, then 2sin \[\frac{A}{2}\cos ec\,\frac{B}{2}\sin \frac{C}{2}-\sin A\cot \frac{B}{2}-\cos A\]is
A)
independent of A, B, done
clear
B)
function of A, B done
clear
C)
function of C done
clear
D)
none of these done
clear
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question_answer5)
If \[y=(1+tan\,A)(1-tan\,B),\]where A-B=\[\frac{\pi }{4}\], then \[{{(y+1)}^{y+1}}\]is equal to
A)
9 done
clear
B)
4 done
clear
C)
27 done
clear
D)
81 done
clear
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question_answer6)
If\[\cos \alpha +\cos \beta =0=sin\alpha +sin\beta ,\]then \[\cos 2\alpha +\cos 2\beta \]is equal to
A)
\[-2\sin (\alpha +\beta )\] done
clear
B)
\[-2\cos (\alpha +\beta )\] done
clear
C)
\[2\sin (\alpha +\beta )\] done
clear
D)
\[2\cos (\alpha +\beta )\] done
clear
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question_answer7)
\[\frac{\sqrt{2}-\sin \alpha -\cos \alpha }{\sin \alpha -\cos \alpha }\]is equal to
A)
\[\sec \left( \frac{\alpha }{2}-\frac{\pi }{8} \right)\] done
clear
B)
\[\cos \left( \frac{\pi }{8}-\frac{\alpha }{2} \right)\] done
clear
C)
\[\tan \left( \frac{\alpha }{2}-\frac{\pi }{8} \right)\] done
clear
D)
\[\cot \left( \frac{\alpha }{2}-\frac{\pi }{2} \right)\] done
clear
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question_answer8)
If \[\alpha =\frac{\pi }{14}\],then the value of (\[\tan \alpha \tan 2\alpha +\tan 2\alpha \tan 4\alpha +\tan 4\alpha \tan \alpha \])is
A)
1 done
clear
B)
1/2 done
clear
C)
2 done
clear
D)
1/3 done
clear
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question_answer9)
The value of expression \[\frac{2(sin{{1}^{o}}+sin{{2}^{o}}+sin{{3}^{o}}+\cdot \cdot \cdot \cdot +\sin {{89}^{o}})}{2(cos{{1}^{o}}+cos{{2}^{o}}+\cdot \cdot \cdot +cos{{44}^{o}})+1}\]Equals
A)
\[\sqrt{2}\] done
clear
B)
\[1/\sqrt{2}\] done
clear
C)
\[1/2\] done
clear
D)
0 done
clear
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question_answer10)
\[\frac{{{\sin }^{2}}A-{{\sin }^{2}}B}{\sin A\cos A-\sin B\cos B}\]is equal to
A)
\[\tan (A-B)\] done
clear
B)
\[\tan (A+B)\] done
clear
C)
\[cot(A-B)\] done
clear
D)
\[cot(A+B)\] done
clear
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question_answer11)
If \[{{\tan }^{2}}\theta =2{{\tan }^{2}}\phi +1\],then \[\cos 2\theta +{{\sin }^{2}}\phi \]equals
A)
-1 done
clear
B)
0 done
clear
C)
1 done
clear
D)
none of these done
clear
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question_answer12)
If A and B are acute postitive angles satisfying the equations 3 \[{{\sin }^{2}}A+2{{\sin }^{2}}B=1\]and 3 \[\sin 2A-2\sin 2B=0\]then A+2B is equal to
A)
\[\pi \] done
clear
B)
\[\frac{\pi }{2}\] done
clear
C)
\[\frac{\pi }{4}\] done
clear
D)
\[\frac{\pi }{6}\] done
clear
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question_answer13)
If \[2\left| \sin 2\alpha \right|=\left| \tan \beta +\cot \beta \right|,\alpha ,\beta \in \left( \frac{\pi }{2},\pi \right)\],then the value of \[\alpha +\beta \]is
A)
\[\frac{3\pi }{4}\] done
clear
B)
\[\pi \] done
clear
C)
\[\frac{3\pi }{2}\] done
clear
D)
\[\frac{5\pi }{4}\] done
clear
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question_answer14)
The most general value for which tan\[\theta \]=-1\[\cos \theta =\frac{1}{\sqrt{2}}\]is (n\[\in \]z)
A)
\[n\pi =\frac{7\pi }{4}\] done
clear
B)
\[n\pi +{{(-1)}^{n}}\frac{7\pi }{4}\] done
clear
C)
\[2n\pi {{+}^{}}\frac{7\pi }{4}\] done
clear
D)
none of these done
clear
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question_answer15)
The number of solutions of \[\sin x+\sin 2x+\sin 3x=\cos x+\cos 2x+\cos 3x,\]\[0\le x\le 2\pi \], is
A)
7 done
clear
B)
5 done
clear
C)
4 done
clear
D)
6 done
clear
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question_answer16)
The sum of all the solutions of \[\cot \theta =\sin 2\theta (\theta \ne n\pi ,n\,integer)\], \[0\le \theta \le \pi \]is
A)
\[3\pi /2\] done
clear
B)
\[\pi \] done
clear
C)
\[3\pi /4\] done
clear
D)
\[2\pi \] done
clear
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question_answer17)
The number of solution of equation \[6\cos 2\theta +2{{\cos }^{2}}(\theta /2)+2si{{n}^{2}}\theta =0,\]\[-\pi <\theta <\pi \]is
A)
3 done
clear
B)
4 done
clear
C)
5 done
clear
D)
6 done
clear
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question_answer18)
Let \[0<{{\theta }_{1}}<{{\theta }_{2}}<{{\theta }_{3}}<...\]denote the positive solution of the equation \[3+3\cos \theta =2{{\sin }^{2}}\theta \]The value of \[{{\theta }_{3}}+{{\theta }_{7}}\]is
A)
6\[\pi \] done
clear
B)
7\[\pi \] done
clear
C)
8\[\pi \] done
clear
D)
4\[\pi \] done
clear
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question_answer19)
The least positive solution of \[\cot \left( \frac{\pi }{3\sqrt{3}}\sin 2x \right)=\sqrt{3}\]lies in
A)
\[\left( 0,\frac{\pi }{6} \right]\] done
clear
B)
\[\left( \frac{\pi }{9},\frac{\pi }{6} \right)\] done
clear
C)
\[\left( \frac{\pi }{12},\frac{\pi }{9} \right]\] done
clear
D)
\[\left( \frac{\pi }{3},\frac{\pi }{2} \right]\] done
clear
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question_answer20)
If \[u=\sqrt{{{a}^{2}}{{\cos }^{2}}\theta +{{b}^{2}}{{\sin }^{2}}\theta }+\sqrt{{{a}^{2}}{{\sin }^{2}}\theta +{{b}^{2}}{{\cos }^{2}}\theta }\]then the difference between the maximum and minimum values of \[{{u}^{2}}\]is given by
A)
\[2({{a}^{2}}+{{b}^{2}})\] done
clear
B)
\[2\sqrt{{{a}^{2}}+{{b}^{2}}}\] done
clear
C)
\[{{(a+b)}^{2}}\] done
clear
D)
\[{{(a-b)}^{2}}\] done
clear
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question_answer21)
IF\[2{{\sin }^{2}}((\pi /2)co{{s}^{2}}x)=1-cos(\pi sin2x),\]\[x\ne (2n+1)\pi /2\],\[n\in I\], then cos 2x is equal to__.
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question_answer22)
The total number of solution of \[{{\sin }^{4}}x+{{\cos }^{4}}x=\sin x\cos x\]in [0,\[2\pi \]] is equal to.
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question_answer23)
Number of solution of equation 2 sin\[\frac{x}{2\,}\,{{\cos }^{2}}x-2\sin \frac{x}{2}{{\sin }^{2}}x={{\cos }^{2}}x-{{\sin }^{2}}x\,\]for \[x\in [0,4\pi ]\]is___.
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question_answer24)
The number of solution to \[\tan x+\sec x=2\cos x\]in [0, 2\[\pi \]) is____.
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question_answer25)
The number of values of x in the interval [0, 3\[\pi \]] satisfying the equation \[2{{\sin }^{2}}x+5\sin x-3=0\]is__.
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