Question 1 :
Value of ${ cos }^{ 2 }{ 135 }^{ \circ  }$
Question 2 :
If $\displaystyle  \cos A+\cos ^2A=1$ then the value of $\displaystyle  \sin ^{2}A+\sin ^{4}A$ is
Question 3 :
Express$\displaystyle \cos { { 79 }^{ o } } +\sec { { 79 }^{ o } }$ in terms of angles between$\displaystyle { 0 }^{ o }$ and$\displaystyle { 45 }^{ o }$
Question 5 :
Simplest form of $\displaystyle \dfrac{1}{\sqrt{2 + \sqrt{2 + \sqrt{2 + 2 cos 4x}}}}$ is
Question 6 :
If $3\sin\theta + 5 \cos\theta =5$, then the value of $5\sin\theta -3 \cos\theta $ are 
Question 7 :
$\left( \dfrac { cosA+cosB }{ sinA-sinB }  \right) ^{ 2014 }+\left( \cfrac { sinA+sinB }{ cosA-cosB }  \right) ^{ 2014 }=...........$
Question 8 :
Find the value of $\sin^3\left( 1099\pi -\dfrac { \pi  }{ 6 }  \right) +\cos^3\left( 50\pi -\dfrac { \pi  }{ 3 }  \right) $
Question 9 :
IF $ \displaystyle \tan \theta =\sqrt{2}    $ , then the value of $ \displaystyle \theta     $ is 
Question 11 :
IF A+B+C=$ \displaystyle 180^{\circ}  $ ,then $  tan A+tanB+tanC $ is equal to
Question 14 :
If$\displaystyle \cot A=\frac{12}{5}$ then the value of$\displaystyle \left ( \sin A+\cos A \right )$ $\displaystyle \times cosec$ $\displaystyle A$ is
Question 17 :
$\tan \theta$ increases as $\theta$ increases.<br/>If true then enter $1$ and if false then enter $0$.<br/>
Question 18 :
As value of $x$ increases from $0$ to $\cfrac{\pi}{2}$, the value of $\cos {x}$:
Question 19 :
If $\sec{2A}=\csc{(A-42^\circ)}$ where $2A$ is acute angle then value of $A$ is
Question 20 :
If $sec\theta -tan\theta =\dfrac{a}{b},$ then the value of $tan\theta $ is
Question 21 :
If $\displaystyle 5\tan \theta =4$, then find the value of $\displaystyle \frac{5\sin \theta -3\cos \theta }{5\sin \theta +2\cos \theta }$. 
Question 22 :
The value of $[\dfrac{\tan 30^{o}.\sin 60^{o}.\csc 30^{o}}{\sec 0^{o}.\cot 60^{o}.\cos 30^{o}}]^{4}$ is equal to
Question 24 :
If $\displaystyle \tan { \theta  } =\frac { 1 }{ 2 } $ and $\displaystyle \tan { \phi  } =\frac { 1 }{ 3 } $, then the value of $\displaystyle \theta +\phi $ is:
Question 26 :
Maximum value of the expression $\begin{vmatrix} 1+{\sin}^{2}x & {\cos}^{2}x & 4\sin2x \\ {\sin}^{2}x & 1+{\cos}^{2}x & 4\sin2x \\ {\sin}^{2}x & {\cos}^{2}x & 1+4\sin2x \end{vmatrix}=$
Question 28 :
Eliminate $\theta$ and find a relation in x, y, a and b for the following question.<br/>If $x = a sec \theta$ and $y = a tan \theta$, find the value of $x^2 - y^2$.
Question 29 :
If $\theta$ increases from $0^0$ to $90^o$, then the value of $\cos\theta$: <br/>
Question 30 :
Which of the following is equal to $\sin x \sec x$?
Question 31 :
If $ \alpha \epsilon \left[ \frac { \pi  }{ 2 } ,\pi  \right] $ then the value of $\sqrt { 1+sin\alpha  } -\sqrt { 1-sin\alpha  } $ is equal to
Question 32 :
If $sin({ 90 }^{ 0 }-\theta )=\dfrac { 3 }{ 7 } $, then $cos\theta $
Question 33 :
Solve : $\dfrac { 2tan{ 30 }^{ \circ  } }{ 1+{ tan }^{ 2 }{ 30 }^{ \circ  } } $
Question 35 :
Given $\cos \theta = \dfrac{\sqrt3}{2}$, which of the following are the possible values of  $\sin 2 \theta$?
Question 37 :
The value of $\sqrt { 3 } \sin { x } +\cos { x } $ is max. when $x$ is equal to
Question 38 :
Select and wire the correct answer from the given alternatives. <br/>$\cos \left(\dfrac {3\pi}{2}+\theta \right)=$ ____
Question 39 :
Given $tan \theta = 1$, which of the following is not equal to tan $\theta$?
Question 40 :
If $\displaystyle x=y\sin \theta \cos \phi ,y=\gamma \sin \theta \sin \phi ,z=\gamma \cos \theta $. Eliminate  $\displaystyle \theta $ and  $\displaystyle \phi $
Question 47 :
The expression$ \displaystyle \left (\tan \Theta +sec\Theta \right )^{2} $ is equal to
Question 48 :
If $\sin \theta + \cos\theta = 1$, then what is the value of $\sin\theta \cos\theta$?
Question 50 :
The solution of $(2 cosx-1)(3+2 cosx)=0$ in the interval $0 \leq \theta \leq 2\pi$ is-
Question 51 :
If $3\cot \theta = 4$ then $\dfrac {5 \sin \theta + 3 \cos \theta}{5 \sin \theta - 3 \cos \theta} = $_____
Question 52 : Match the following columns with the values obtained for the solution.<br/><table class="wysiwyg-table"><tbody><tr><td>$I.$<br/>$x\cos \theta+ y\sin \theta=a$,<br/>$x\sin \theta- y\cos \theta=b$<br/></td><td><br/>$a)$ $(x^{2}-y^{2})^{2}=16xy$ <br/><br/></td></tr><tr><td>$II.$<br/>$x= \sec \theta+\tan\theta$,<br/>$y=\sec\theta-\tan\theta$<br/></td><td>$b)$ $xy = 1$<br/></td></tr><tr><td>$III.$<br/>$x\sec \theta+ y\tan \theta=a$,<br/>$x\tan \theta+ y\sec \theta=b$<br/></td><td><br/> $c)$ $x^{2}-y^{2}=a^{2}-b^{2}$<br/><br/></td></tr><tr><td><br/>$IV.$ <br/>$x=\cot\theta+\cos\theta$,<br/>$y=\cot\theta-\cos\theta$<br/></td><td><br/> $d)$ $x^{2}+y^{2}=a^{2}+b^{2}$<br/><br/></td></tr></tbody></table><br/>
Question 53 :
The value of$\tan {203^ \circ } + \tan {22^ \circ } + \tan {203^ \circ }\tan {22^ \circ }$ is
Question 54 :
If $\displaystyle \sec \theta +\tan \theta=p$, then find the value of $\tan \theta$.<br/>
Question 57 :
If $\sin A, \cos A$ and $\tan A$ are in Geometric progression, then $\cot^6A-\cot^2 A$ is
Question 58 :
If $\sin \theta, \cos \theta, \tan \theta$ are in $G.P$, then $\cos^{9}\theta+\cos^{6}\theta+3\cos^{5}\theta-1$ is equal to:<br/>
Question 59 :
If A + B + C = ${ 180 }^{ o }$ then sin (A + B)=
Question 60 :
If $A$ and $B$ are acute angles such that $\sin A=\sin^2 B, 2\cos^2 A=3 \cos^2 B$; then
Question 61 :
If $\cos {\theta _1} = 2\cos {\theta _2},$ then $\tan \dfrac{{{\theta _1} - {\theta _2}}}{2}$. $\tan \dfrac{{{\theta _1} + {\theta _2}}}{2}$ is equal to
Question 63 :
If $\sin ^{2}\theta _{1}+\sin ^{2}\theta _{2}+\sin ^{2}\theta _{3}=0$, then which of the following is NOT the possible value of $\cos ^{2}\theta _{1}+\cos ^{2}\theta _{2}+\cos ^{2}\theta _{3}$.<br/>
Question 64 :
Evaluate: $\cfrac { \sin { \theta  } \cos { \theta  } \sin { \left( { 90 }^{ o }-\theta  \right)  }  }{ \cos { \left( { 90 }^{ o }-\theta  \right)  }  } +\cfrac { \cos { \theta  } \sin { \theta  } \cos { \left( { 90 }^{ o }-\theta  \right)  }  }{ \sin { \left( { 90 }^{ o }-\theta  \right)  }  } +\cfrac { \sin ^{ 2 }{ { 27 }^{ o } } +\sin ^{ 2 }{ { 63 }^{ o } }  }{ \cos ^{ 2 }{ { 40 }^{ o } } +\cos ^{ 2 }{ { 50 }^{ o } }  } $
Question 65 :
If $\cos\theta = \dfrac{14}{4}$ and $\sin\theta$ $=$ $\dfrac{8}{3}$, what is the value of $\cot\theta$?<br/>
Question 66 :
If $\sin \theta + \cos \theta = \sqrt {2}$, find the value of $\sin \theta \times \cos \theta$.
Question 67 :
Let $\displaystyle a=cosx + cos(x + \frac{2{\pi}}{3}) + cos(x + \frac{4{\pi}}{3})$ and $\displaystyle b=sinx + sin(x + \frac{2{\pi}}{3}) + sin(x + \frac{4{\pi}}{3})$ then which one of the following holds good ?
Question 68 :
$\dfrac{2 \sin \theta \, \tan \theta (1 - \tan \theta) + 2 \sin \theta \, \sec^2 \theta}{(1 + \tan \theta)^2}$ =
Question 69 :
The value of $\cot 1^{\circ} \cot 2^{\circ} .... \cot 89^{\circ}$ is .....
Question 70 :
The number of solutions of $\sin^{2}\theta + 3\cos \theta = 3$ in $[-\pi, \pi]$, is
Question 71 :
$\displaystyle \left (\frac{\sin\, 50^{\circ}}{\cos\, 40^{\circ}} \right)^{2}\, +\, \left (\frac{\cos\, 28^{\circ}}{\sin\, 62^{\circ}} \right)^{2}\, -\, 2\, \tan^{2}\, 45^{\circ}$
Question 72 :
If $\displaystyle \sec 2A=\text{cosec } \left ( A-42^{\circ} \right )$ where $2A$ is acute angle, then value of $A$ is
Question 73 :
If $\tan 1^o \tan 2^o ... \tan 89^o=x^2-8$, then the value of $ x$ can be<br/>
Question 74 :
When$\displaystyle \theta =\frac{11}{3}\pi $ then the value of$\displaystyle \left ( \cos \theta -\sin \theta \right )$ is
Question 75 :
The value of $\sin 12^{\circ} \sin 48^{\circ} \sin 54^{\circ}$ is equal to.
Question 76 :
If $p=\sec\alpha-\tan\alpha , q = \text{cosec }\alpha+\cot\alpha$. Find $q$ in terms of $ p$.<br/>
Question 78 :
If $\theta =\dfrac{\pi}{2^n+1}$, then the value of $\cos\theta \cos 2\theta \cos 2^2\theta$------$\cos 2^{n-1}\theta$ is?
Question 79 :
The maximum value of<br/>$\cos x\,\left(\displaystyle \dfrac{\cos x}{1-\sin x}+\dfrac{1-\sin x}{\cos x}\right)$ is <br/>
Question 80 :
Choose the correct answer and justify.<br>$\quad (1+\tan\theta+\sec\theta)(1+\cot\theta - cosec\theta) = $
Question 82 :
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 83 :
Find the value of $\tan 10^{\circ} \tan 15^{\circ} \tan 75^{\circ} \tan 80^{\circ} $
Question 86 :
The value of$ \displaystyle \tan 1^{\circ}\tan 2^{\circ}\tan 3^{\circ}.....\tan 89^{\circ} $ is
Question 87 :
If $ \displaystyle  \cos \theta -\sin \theta =\sqrt{2} \sin \theta $ , then  $ \cos \theta +\sin \theta $ is
Question 88 :
Is LHS=RHS?$\displaystyle\frac{\tan^2\theta}{1+\tan^2\theta}+\displaystyle\frac{\cot^3\theta}{1+\cot^2\theta} = \sec\theta sin\theta - 2 cosec\theta\cos\theta$Say true or false.
Question 89 :
If $A$ and $B$ are complimentary angles, then $\sin A \times \sec B =$
Question 91 :
Evaluate: $\cfrac { \cos ^{ 2 }{ { 20 }^{ o } } +\cos ^{ 2 }{ { 70 }^{ o } }  }{ \sec ^{ 2 }{ { 50 }^{ o } } -\cot ^{ 2 }{ { 40 }^{ o } }  } +2\text{cosec} ^{ 2 }{ { 58 }^{ o } } -2\cot { { 58 }^{ o } } \tan { { 32 }^{ o } } -4\tan { { 13 }^{ o } } \tan { { 37 }^{ o } } \tan { { 45 }^{ o } } \tan { { 53 }^{ o } } \tan { { 77 }^{ o } } $
Question 93 :
If$\displaystyle 3\tan { \theta } =4$, then$\displaystyle \sin { \theta }$ is :
Question 95 :
The value of $\displaystyle \frac { 2\cos { { 67 }^{ o } }  }{ \sin { { 23 }^{ o } }  } -\frac { \tan { { 40 }^{ o } }  }{ \cot { { 50 }^{ o } }  } -\sin { { 90 }^{ o } } $ is :
Question 96 :
$\sin ^{ 2 }{ A } \cos ^{ 2 }{ B } -\cos ^{ 2 }{ A } \sin ^{ 2 }{ B }$ simplifies to
Question 97 :
If $\tan A = \displaystyle\dfrac{3}{4}$ and $A+B = 90^{\small\circ}$, then what is the value of $\cot B$?
Question 98 :
$\tan 1^{\circ} \tan 2^{\circ} \tan 3^{\circ} ... \tan 89^{\circ} = $
Question 99 :
Evaluate: $\sin { \left( { 50 }^{ o }+\theta  \right)  } -\cos { \left( { 40 }^{ o }-\theta  \right)  } +\tan {1}^{o} \tan {10}^{o} \tan {20}^{o} \tan {70}^{o} \tan {80}^{o} \tan {89}^{o}$
Question 100 :
If $\displaystyle \sin \left ( A+B \right ) =\frac{\sqrt{3}}{2}$ and $\displaystyle \cot \left ( A-B \right )=1$, then find $A$
Question 101 :
If $\tan { \theta  } +\sin { \theta  } =m, \tan { \theta - \sin { \theta =n }  } $, then $(m^{2}-n^{2})^{2}=$.<br/>
Question 103 :
If $\displaystyle \sin \theta+\sin ^{2} \theta +\sin ^{3}\theta= 1$ then the value of $\displaystyle \cos ^{6}\theta-4\cos ^{4}\theta+8\cos ^{2}\theta$ equals<br/>
Question 104 :
If $\displaystyle \left ( \sec \theta +\tan \theta  \right )\left ( \sec \phi +\tan \phi  \right )\left ( \sec \psi  +\tan \psi  \right )=\tan \theta \tan \phi \tan \psi $ ,then $\displaystyle \left ( \sec \theta -\tan \theta  \right )\left ( \sec \phi -\tan \phi  \right )\left ( \sec \psi  -\tan \psi  \right )$ is equal to <br/>
Question 105 :
If $\displaystyle \frac{\sin x}{a}= \frac{\cos x}{b}= \frac{\tan x}{c}= k,$ then $\displaystyle bc+\frac{1}{ck}+\frac{ak}{1+bk} $ is equal to<br><br><br>
Question 106 :
Let $\displaystyle 0\leq \theta \leq \frac{\pi}{2}$ and $\displaystyle x=Xcos \: \theta +Ysin\: \theta ,y=Xsin\: \theta -Ycos\: \theta $ such that<br>$\displaystyle x^{2}+4xy+y^{2}=aX^{2}+bY^{2},$ where $\displaystyle a,b$ are constants. Then<br>
Question 107 :
In $\displaystyle A_{n}=\cos^{n}\theta+\sin^{n}\theta, n\in N$ and $\displaystyle \theta \in R$<br/><br/>If $\displaystyle A_{n-4}-A_{n-2}=\sin^{2}\theta\cos^{2}\theta A_{\lambda} $ , then $\displaystyle \lambda $ equals<br/>
Question 108 :
Assertion: Statement 1:If $\displaystyle x+y+z= xyz,$ then at most one of the numbers can be negative.
Reason: Statement 2: In a triangle ABC, $\displaystyle \tan A+\tan B+\tan C= \tan A \tan B \tan C $ ,there can be at most one obtuse angle in a triangle.
Question 109 :
If $\sin {x}+\sin^{2}{x}+\sin^{3}{x}=1 ,\ \ then \ \  \cos^{6}{x}-4\cos^{4}{x}<br/>+8\cos^{2}{x}$ is equal to<br/>
Question 110 :
Let $x=(1+\sin A)(1-\sin B)(1+\sin C), y=(1-\sin A)(1-\sin B)(1-\sin C)$ and if $x=y$, then
Question 111 :
The number of ordered pairs $(\alpha, \beta)$, where $\alpha, \beta $ $\in$ $(-\pi, \pi)$ satisfying $\cos(\alpha -\beta)=1$ and $\cos(\alpha+\beta)=\dfrac {1}{e}$ is
Question 112 :
If $3 \sin\theta+ 5 \cos\theta=5$, then $5 \sin\theta-3 \cos\theta$ is equal to<br/>
Question 113 :
In atriangle $ABC$, $\sin A\cos B=\dfrac{1}{4}$ and $3\tan A=\tan B$ , the triangle is
Question 115 :
If $x_{1}=1$ and $x_{n+1}=\frac{1}{x_{n}}\left ( \sqrt{1+x_{n}^{2}}-1 \right ),n\geq 1,n \in N$, then $x_{n}$ is equal to :<br>
Question 116 :
If $\sin (\alpha+\beta)=1$ and $\sin(\alpha -\beta)=1/2$ where $\alpha, \beta \epsilon [0, \pi /2]$ then
Question 117 :
If the quadratic equation $ax^2+bx+c=0$ ($a > 0$) has $\sec^2\theta$ and $\text{cosec}^2\theta$ as its roots, then which of the following must hold good?<br>
Question 119 :
If $\sin (\alpha+\beta)=1$ and $\sin(\alpha -\beta)=1/2$ where $\alpha, \beta \epsilon [0, \pi /2]$ then
Question 120 :
If the angles of a triangle are in arithmetic progression such that $\sin (2A+B)=\dfrac{1}{2}$, then
Question 121 :
If $5\cos { A } =4\sin { A } $, then $\tan { A=\_ \_ \_ } $
Question 122 :
If $\sin x+\sin ^{2}x=1$,thenthe value of $\cos ^{12}x+3\cos ^{10}x+3\cos ^{8}x+\cos ^{6}x-2$ is equal to
Question 123 :
The value of $\displaystyle \frac { \sin { { 70 }^{ o } }  }{ \cos { { 20 }^{ o } }  } +\frac { \text{cosec }{ 20 }^{ o } }{ \sec { { 70 }^{ o } }  } -2\cos { { 70 }^{ o } } \text{cosec }{ 20 }^{ o }$ is :
Question 124 :
If $\sin A, \cos A$ and $\tan A$ are in G.P. then $\cot^6 A- \cot^2A$ is equal to
Question 125 :
$\cos { { 1 }^{ o } } .\cos { { 2 }^{ o } } .\cos { { 3 }^{ o } } ......\cos { { 179 }^{ o } } $ is equal to
Question 126 :
If $0\leq x, y\leq 180^o$ and $\sin (x-y)=\cos(x+y)=\dfrac 12$, then the values of $x$ and $y$ are given by
Question 127 :
Which one of the following when simplified is not equal to one?
Question 129 :
If $\displaystyle \frac { \sin ^{ 4 }{ x }  }{ 2 } +\frac { \cos ^{ 4 }{ x }  }{ 3 } =\frac { 1 }{ 5 } ,$ then:
Question 131 :
$1)$ lf $\mathrm{x}$ lies in the lst quadrant and<br/>$\cos \mathrm{x}+\cos 3\mathrm{x}=\cos 2\mathrm{x}$ then $\mathrm{x}=30^{\mathrm{o}}$ or $45^{\mathrm{o}}$<br/>$2)\mathrm{x}\in(0,2\pi)$ and cosec $\mathrm{x}+2=0$ then $x=\displaystyle \frac{7\pi}{6},\frac{l1\pi}{6}$<br/>$3)\mathrm{x}\in[0,2\pi]$ and $(2 \cos \mathrm{x}- \mathrm{l}) (3+2\cos \mathrm{x})=0$ then $\displaystyle \mathrm{x}=\frac{\pi}{3}$ , $\displaystyle \frac{5\pi}{3}$ Which of the above statements are correct?<br/>
Question 134 :
For all real values of $\theta$ , $\cot\theta-2 \cot 2\theta$ is equal to
Question 138 :
In $\triangle ABC, \angle B = 90^{\circ}, BC = 7$ and $AC - AB = 1$, then $\cos C = .....$
Question 139 :
If $\displaystyle\frac{\cos^{4}x }{\theta _{1}}+\displaystyle\frac{\sin^{4}x}{\theta _{2}}=\frac{1}{\theta _{1}+\theta _{2}},$ then $\displaystyle\frac{\theta _{2}}{\theta _{1}}$ equals<br>
Question 142 :
Let $\displaystyle -\frac { \pi }{ 6 } <\theta <-\frac { \pi }{ 12 }$, Suppose$\displaystyle { \alpha }_{ 1 }$ and$\displaystyle { \beta }_{ 1 }$ are the roots of the equation$\displaystyle { x }^{ 2 }-2x\sec { \theta } +1=0$ and$\displaystyle { \alpha }_{ 2 }$ and $\displaystyle { \beta }_{ 2 }$ are the roots of the equation$\displaystyle { x }^{ 2 }+2x\tan { \theta } -1=0$. If$\displaystyle { \alpha }_{ 1 }>{ \beta }_{ 1 }$ and$\displaystyle { \alpha }_{ 2 }>{ \beta }_{ 2 }$, then$\displaystyle { \alpha }_{ 1 }+{ \beta }_{ 2 }$ equals to
Question 143 :
If $16\cot \theta = 12$, then $\dfrac {\sin \theta - \cos \theta}{\sin \theta + \cos \theta} = $ _____
Question 144 :
In $\triangle ABC$, the measure of $\angle B$ is $90^{\circ}, BC = 16$, and $AC = 20$. $\triangle DEF$ is similar to $\triangle ABC$, where vertices $D, E,$ and $F$ correspond to vertices. $A, B$, and $C$, respectively, and each side of $\triangle DEF$ is $\dfrac {1}{3}$ the length of the corresponding side of $\triangle ABC$. What is the value of $\sin F$?
Question 146 :
In a $\Delta ABC$, if $\cos A \cos B \cos C=\displaystyle\dfrac {\sqrt 3-1}{8}$ and $\sin A. \sin B. \sin C=\displaystyle \dfrac {3+\sqrt 3}{8}$, then- On the basis of above information, answer the following questions:The angles of $\Delta ABC$ are:<br/>
Question 147 :
The value of the expression $(\tan1^{0} \tan2^{0} \tan 3^{0}...\tan89^{0})$ is equal to<br/>
Question 148 :
<br/>If $a \sin^{2}\theta+b\cos^{2}\theta=a\cos^{2}\phi+b\sin^{2}\phi=1$ and $a \tan\theta=b\tan\phi$, then choose the correct option.<br/>
Question 149 :
In a right angle triangle $\triangle ABC,\,\sin ^{ 2 }{ A } +\sin ^{ 2 }{ B } +\sin ^{ 2 }{ C } $ is
Question 150 :
Assertion: In a triangle ABC if a, b, c are in A.P., then $\displaystyle \cot \frac{A}{2}\cot \frac{C}{2}=2$
Reason: Three numbers a, b, c are in A.P. if $ a+ c = 2b$.
