Question 1 :
The value of $4\cos^{2} \dfrac {\pi}{3} + \sec^{2} \dfrac {\pi}{6} - \sin^{2} \dfrac {\pi}{4}$ is
Question 3 : <div>State whether the following statement is true or false:<br/></div>$4\cos \theta - 3\sec \theta = 2\tan \theta$.
Question 4 : Express in Degrees:<br/>$(a) \displaystyle \left ( \frac{2 \pi}{15} \right )^{c}$<div>$(b) \displaystyle (-2)^{c}$</div>
Question 5 :
The principle solution of the $Cos\theta = - \frac{1}{2}$ is <br/>
Question 6 :
If $ \displaystyle \sin \Theta +\cos \Theta =\sqrt{2,} and \Theta $ is actual , then $ \displaystyle \tan \Theta $ is equal to
Question 8 :
What is the value of $\dfrac {(\cos 10^{o}+\sin 20^{o})}{(\cos 20^{o}-\sin 10^{o})}$?
Question 9 :
If $\tan 45^{\circ} = \cot \theta$, then the value of $\theta$, in radians is
Question 10 :
The value of $\cot 15^{\circ} \cot 20^{\circ} \cot 70^{\circ} \cot 75^{\circ}$ is equal to
Question 12 :
Evaluate $8 \sqrt{3} \, \text{cosec}^2 30^o \, \sin \, 60^o \, \cos \, 60^o \, \cos^2 45^o \, \sin \, 45^o \, \tan \, 30^o \, \text{cosec}^3 45^o$
Question 14 :
If $\tan\theta +\cot\theta =2$, then the value of $\tan^2\theta +\cot^2\theta$ is __________?
Question 15 :
If P = cos $\dfrac {\pi } {20} .cos \dfrac {3\pi } {20} .cos\dfrac {7\pi } {20} . cos\dfrac{9\pi } {20} $ & Q = cos$ \dfrac{\pi } {11}. cos\dfrac{2\pi } {11} .cos\dfrac{4\pi } {11} . cos\dfrac {8\pi } {11}. cos \dfrac {16\pi } {11}, then \dfrac {P} {Q} $ is
Question 17 :
If tan A = 4 /3, tanB = 1/ 7,then A - B =
Question 20 :
The minimum value of $\sec^2 \theta + \cos^2 \theta$ is -<br/>
Question 21 :
The number of value $x$ in the interval $[0,3\pi]$ satisfying the $eq^n 2\sin^2x+5\sin \,\,x-3=0$ is
Question 23 : <div>State True or False</div><div> $\cos 2{ A } =\cos ^{ 2 }{ A } -\sin ^{ 2 }{ A } $</div>
Question 24 :
In $\sin \theta = \dfrac{{ - 1}}{{\sqrt 2 }}\& \;\tan \;\theta $ lies in which quadrant?
Question 27 :
$\dfrac { \cos { \theta +\sin { \theta } } }{ \cos { \theta -\sin { \theta } } } =$
Question 29 :
$\cfrac { \tan { \theta } }{ \sec { \theta } -1 } +\cfrac { \tan { \theta } }{ \sec { \theta } +1 } $ is equal to
Question 31 :
If $sin2x-2cosx=0$ .Then the number of values of $\theta$ lying in $[0, \pi]$ is?
Question 37 :
Given that $ \displaystyle \cos 50^{\circ}18'=0.6388\ and\ \cos 50^{\circ}42'=0.6334, $ then the possible value of $ \displaystyle \cos 50^{\circ}20' $ is
Question 41 :
If $0<x<\pi$ , and $\cos { x } +\sin { x } =\cfrac { 1 }{ 2 }$, then $\tan { x } $ is -<br><br>
Question 44 :
If $ \dfrac{ \sin A}{ \sin B} = \dfrac{\sqrt{3}}{2}$ and $\dfrac{ \cos A}{\cos B} = \dfrac{\sqrt{5}}{2},\; 0<A,\; B< \pi/2, $ then $ \tan A+ \tan B$ is equal to
Question 47 :
If $\cot\left( {a + \beta } \right) = 0,$ then $\sin\left( {a + 2\beta } \right)$ can be
Question 48 :
The value of $\sin ^{ 2 }{ { 29 }^{ o } } +\cos ^{ 2}{ { 29 }^{ o } } $ will be:
Question 49 :
Find the value of $\dfrac{sin (-660^o) tan (1050^o) sec (-420^o)}{cos (225^o ) cosec (315^o) cos(510^o)}$
Question 50 :
If $\displaystyle \sin B=\frac{1}{2}$ what is the value of $\displaystyle 3\cos B-4\cos ^{3}B?$
Question 52 :
<b>If</b> $A=\left\{ x\epsilon R/\frac { \pi }{ 4 } \le x\le \frac { \pi }{ 3 } \right\} \quad$<b>and </b>$f(x)=\sin { x } -x\quad$, <b>then </b>$f(A)=$
Question 53 :
$\dfrac{{\tan\theta }}{{1 - \cot \theta }} + \dfrac{{\cot \theta }}{{1 - \tan \theta }} = 1 + \sec \theta .\text{cosec}\theta $
Question 54 :
If $\sqrt {3}\cos^{2}\theta -2\sqrt {3}\sin \theta \cos \theta -3\sin^{2}\theta =0$, then
Question 55 :
The value of $cosycos\left( \cfrac { \pi }{ 2 } -x \right) -cos\left( \cfrac { \pi }{ 2 } -y \right) cosx+sinycos\left( \cfrac { \pi }{ 2 } -x \right) +cosxsin\left( \cfrac { \pi }{ 2 } -y \right)$ is zero if
Question 56 :
Let $f\left( x \right) = \sqrt {\cot \left( {5 + 3x} \right)\left( {\cot \left( 5 \right) + \cot \left( {3x} \right)} \right) - \sqrt {\cot 3x} + 1} $, the domain is
Question 58 :
If $A + B = \dfrac { \pi } { 4 }$ then value of $( 1 + \tan A ) ( 1 + \tan B ) =$
Question 59 :
$\sin 20^{\circ} \sin 24^{\circ} \sin 48^{\circ} \sin 84^{\circ}$ is equal to
Question 60 :
If $\left (\alpha+\beta\right )=\dfrac {\pi}{ 2}$ and $\left (\beta+\gamma\right )=\alpha$, then $tan\alpha$ equals
Question 62 :
<br>$A$ vertical tower stands on a declivity which isinclined at $15^{0}$ to the horizon. From the foot of the tower a man ascends the declivity for80 feet and then finds that the tower subtends an angle of $30^{0}$. The height of the tower is<br>
Question 63 :
Given that $\tan (A + B) = \dfrac{\tan A + \tan B}{1 - \tan A \tan B}$ where $A$ and $B$ are acute angle.<br/>Calculate $A + B$ when $\tan A = \dfrac{1}{2}, \tan B = \dfrac{1}{3}$.
Question 64 :
If $\sin { \alpha } +\sin { \beta } =0=\cos { \alpha } +\cos { \beta } $, where $0<\beta <\alpha <2\pi $, then which of the following is correct?
Question 66 :
The equation $\sin { 2x } +\cos { 2x } +\sin { x } +\cos { x } +1=0$ has no solution in:
Question 69 :
If $y=\tan 3x.\cot x$ then which of the following values is not possible for $y$?<br>
Question 71 :
The sum of all the solution of equation $\displaystyle \sin{\pi}x + \cos{\pi}x = 0 $ if $x \in [0, 100], $ is<br/>
Question 72 :
Statement 1 : lf $x\cos\theta=y\cos(120^{0}+\theta)= z\cos (\theta+240^{0})$, then $xy+yz+xz=0$<br>Statement 11 :Value of $\cos\alpha+\cos(120^{0}+\alpha)+\cos(120^{0}-\alpha)=0$ <br>Then which of the above statements is correct?<br><br><br>
Question 73 : <div>State true or false.</div>If $A+B+C=\pi$ then ${\sin ^3}A\cos (B - C) + \sin{^3}B\cos (C - A) + \sin{^3}C\cos (A - B)=3$
Question 74 :
The number of solution of the equation $1+\sin\,x\,\sin^2\left (\dfrac{x}{2}\right)=0, -\pi,\, \pi$ is -
Question 78 :
$4\sin \left( {{{420}^0} - a} \right)\cos \left( {60 + a} \right) = $
Question 79 :
The equation $\displaystyle 2 \sin \frac{x}{2} \cos^2 x - 2 \sin \frac{x}{2} \sin^2 x = \cos^2 x - \sin^2 x$ has a root for which
Question 80 :
The value of the expression $\left [ \cfrac{\sin^{2} 22^{0}+ \sin^{2} 68^{0}}{\cos^{2} 22^{0}+ \cos^{2} 68^{0}}+\sin^{2} 63^{0} + \cos 63^{0} \sin 27^{0} \right ]$ is<br/>
Question 81 :
$\dfrac{{\cot x}}{{\cot x - \cot 3x}} + \dfrac{{\tan x}}{{\tan x - \tan 3x}} = $
Question 82 :
The number of points of intersection of two curves $y=2 \sin x$ and $y=5x^2+2x+3$ is<br>
Question 85 :
If $5\cos x+12\cos y=13$, then the maximum value of $5\sin x+12\sin y=?$
Question 86 :
If $\displaystyle 0\le x\le \pi $ and $\displaystyle { 81 }^{ { \sin }^{ 2 }x }+{ 81 }^{ { \cos }^{ 2 }x }=30$, then $x$ is equal to:
Question 87 :
If $\displaystyle \theta \in \left ( 0,\frac{\pi }{2} \right )$, then the value of $\displaystyle \cos \left ( \theta -\frac{\pi }{4} \right )$ lies in the interval
Question 88 :
If $0< x\leq \cfrac {\pi}{2}$, then $(\sin x+ \text{cosec} x)$ is greater than or equal to
Question 89 :
If $\left (\alpha + \beta\right ) = \dfrac {\pi}{2}$ and $\left (\beta + \gamma\right ) = \alpha$, then $\tan \alpha$ equals
Question 90 :
The value of $ \cos 60^{\circ} \sin 30^{\circ}+ \sin 60^{\circ} \cos30^{\circ}$ is :<br/>
Question 93 :
If $\displaystyle \cos { 2B } =\frac { \cos { \left( A+C \right) } }{ \cos { \left( A-C \right) } } $, then $\tan { A } ,\tan { B } ,\tan { C } $ are in
Question 95 :
The maximum value of $\left( {\cos {\alpha _1}} \right).\left( {\cos {\alpha _2}} \right).....\left( {\cos {\alpha _n}} \right)$ under the restriction $0 \le {\alpha _1},{\alpha _2},..........{\alpha _a} \le \pi /2$ and $\left( {\cot {\alpha _1}} \right).\left( {\cot {\alpha _2}} \right).......\left( {\cot {\alpha _n}} \right) = 1$
Question 96 :
If $k_1=\tan 27\theta-\tan \theta$ and $k_2=\dfrac {\sin\theta}{\cos 3\theta}+\dfrac {\sin 3\theta}{\cos 9\theta}+\dfrac {\sin 9\theta}{\cos 27\theta}$ , then<br/>
Question 97 : <div><div>State whether the following statement is true or false.</div></div>$\dfrac { \sin { x } -\sin { y } }{ \cos { x } +\cos { y } } =\tan { \left( \dfrac { x-y }{ 2 } \right) }$
Question 98 :
Whether the given equation : $\frac{{\sin 2x}}{{2 \cos x}} = \tan x$ is ?
