Question 1 :
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 3 :
If $3\sin\theta + 5 \cos\theta =5$, then the value of $5\sin\theta -3 \cos\theta $ are 
Question 6 :
Express$\displaystyle \cos { { 79 }^{ o } } +\sec { { 79 }^{ o } }$ in terms of angles between$\displaystyle { 0 }^{ o }$ and$\displaystyle { 45 }^{ o }$
Question 7 :
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 9 :
If $\displaystyle  \cos A+\cos ^2A=1$ then the value of $\displaystyle  \sin ^{2}A+\sin ^{4}A$ is
Question 10 :
Which of the following is equal to $\sin x \sec x$?
Question 11 :
If $\sec{2A}=\csc{(A-42^\circ)}$ where $2A$ is acute angle then value of $A$ is
Question 12 :
The solution of $(2 cosx-1)(3+2 cosx)=0$ in the interval $0 \leq \theta \leq 2\pi$ is-
Question 13 :
If $\sin \theta + \cos\theta = 1$, then what is the value of $\sin\theta \cos\theta$?
Question 18 :
find whether ${ \left( \sin { \theta  } +co\sec { \theta  }  \right)  }^{ 2 }+{ \left( \cos { \theta  } +\sec { \theta  }  \right)  }^{ 2 }=7+\tan ^{ 2 }{ \theta  } +\cos ^{ 2 }{ \theta  } $ is true or false.
Question 19 :
$\left( \dfrac { cosA+cosB }{ sinA-sinB }  \right) ^{ 2014 }+\left( \cfrac { sinA+sinB }{ cosA-cosB }  \right) ^{ 2014 }=...........$
Question 20 :
As value of $x$ increases from $0$ to $\cfrac{\pi}{2}$, the value of $\cos {x}$:
Question 21 :
Given $tan \theta = 1$, which of the following is not equal to tan $\theta$?
Question 24 :
Find the value of $\sin^3\left( 1099\pi -\dfrac { \pi  }{ 6 }  \right) +\cos^3\left( 50\pi -\dfrac { \pi  }{ 3 }  \right) $
Question 26 :
IF A+B+C=$ \displaystyle 180^{\circ}  $ ,then $  tan A+tanB+tanC $ is equal to
Question 29 :
If $sin({ 90 }^{ 0 }-\theta )=\dfrac { 3 }{ 7 } $, then $cos\theta $
Question 30 :
Simplest form of $\displaystyle \dfrac{1}{\sqrt{2 + \sqrt{2 + \sqrt{2 + 2 cos 4x}}}}$ is
Question 32 :
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 33 :
If $\displaystyle \tan { \theta  } =\frac { 1 }{ 2 } $ and $\displaystyle \tan { \phi  } =\frac { 1 }{ 3 } $, then the value of $\displaystyle \theta +\phi $ is:
Question 34 :
Solve : $\dfrac { 2tan{ 30 }^{ \circ  } }{ 1+{ tan }^{ 2 }{ 30 }^{ \circ  } } $
Question 35 :
IF $ \displaystyle \tan \theta =\sqrt{2}    $ , then the value of $ \displaystyle \theta     $ is 
Question 37 :
The value of $\sqrt { 3 } \sin { x } +\cos { x } $ is max. when $x$ is equal to
Question 38 :
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 39 :
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 40 :
$\tan \theta$ increases as $\theta$ increases.<br/>If true then enter $1$ and if false then enter $0$.<br/>
Question 41 :
If $\tan \theta = \dfrac {4}{3}$ then $\cos \theta$ will be
Question 42 :
Solve:$\displaystyle \sin ^{4}\theta +2\cos ^{2}\theta \left ( 1-\frac{1}{\sec ^{2}\theta } \right )+\cos ^{4}\theta $
Question 43 :
The angle of elevation and angle of depression both are measured with
Question 46 :
If $\theta$ increases from $0^0$ to $90^o$, then the value of $\cos\theta$: <br/>
Question 47 :
The given expression is $\displaystyle \sin { \theta  } \cos { \left( { 90 }^{ o }-\theta  \right)  } +\cos { \theta  } \sin { \left( { 90 }^{ o }-\theta  \right)  } +4 $ equal to :<br/>
Question 48 :
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 49 :
Find the value of $ \displaystyle  \theta , cos\theta  \sqrt{\sec ^{2}\theta -1}     = 0$
Question 51 :
Choose the correct answer and justify.<br>$\quad (1+\tan\theta+\sec\theta)(1+\cot\theta - cosec\theta) = $
Question 53 :
If $ \sqrt3 \cos \theta + \sin \theta = \sqrt2 , $ then the most general value of $ \theta $ is :
Question 54 :
$\tan 1^{\circ} \tan 2^{\circ} \tan 3^{\circ} ... \tan 89^{\circ} = $
Question 55 :
The value of $\cot 1^{\circ} \cot 2^{\circ} .... \cot 89^{\circ}$ is .....
Question 56 :
If co$\displaystyle \sec \left ( 20^{\circ} + x \right )=\sec \left ( 50^{\circ}+x \right ) $ the value of x is
Question 57 :
If $\sec \theta + \tan \theta = p$ then $\sin \theta = \frac { p ^ { 2 } + 1 } { p ^ { 2 } - 1 }$ 
Question 58 :
The value of $\sin 12^{\circ} \sin 48^{\circ} \sin 54^{\circ}$ is equal to.
Question 59 :
Solve : $4\sin x \cos x + 2 \sin x + 2 \cos x + 1 = 0$
Question 61 :
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 62 :
If $\left( 1+\tan { \theta } \right) \left( 1+\tan { \phi } \right) =2$, then $\left( \theta +\phi \right) $ is equal to
Question 65 :
If $'\theta '$  is in the III quadrant then  $\sqrt{4  \sin^{4}\theta }+4  \cos^{2}\left ( \frac{\pi }{4}-\frac{\theta }{2} \right )=$<br/>
Question 69 :
Find the value of : $\dfrac {\cos 38^{\circ} \csc 52^{\circ}}{\tan 18^{\circ} \tan 35^{\circ} \tan 60^{\circ} \tan 72^{\circ} \tan 55^{\circ}} =$
Question 72 :
If $\sin A, \cos A$ and $\tan A$ are in Geometric progression, then $\cot^6A-\cot^2 A$ is
Question 73 :
If $ \displaystyle  \cos \theta -\sin \theta =\sqrt{2} \sin \theta $ , then  $ \cos \theta +\sin \theta $ is
Question 74 :
If $7 \theta $ and $2 \theta$ are measure of acute angles such that  sin $7\theta$=cos $2 \theta$, then $2sin 3\theta-\sqrt3$ tan $3\theta$ is ________.
Question 75 :
If$\displaystyle \sin \theta +\sin ^{2}\theta =1$ then the value of$\displaystyle \cos ^{12}\theta +3\cos ^{10}\theta +3\cos ^{8}\theta +\cos ^{6}\theta +2\cos ^{4}\theta +2\cos ^{2}\theta -2$ is _________
Question 76 :
Check whether the statement is true/false <br/>$\sec ^ { 2 } \theta + cosec ^ { 2 } \theta = \sec ^ { 2 } \theta \cdot \sin ^ { 2 } \theta$
Question 77 :
What is $\dfrac{\cot 224^o - \cot 134^o}{\cot 226^o + \cot 316^o}$ equal to ?
Question 78 :
If 2 sin $x^{\circ}\,-\,1\,=\,0$ and $x^{\circ}$ is an acute angle;$tan\,x^{\circ}$ is $\displaystyle\,\frac{1}{m}$, m is
Question 81 :
$\dfrac {\cos (90 -\theta) \sec (90 - \theta)\tan \theta}{\text{cosec } (90 - \theta)\sin (90 - \theta) \cot (90 - \theta)} + \dfrac {\tan (90 - \theta)}{\cot \theta} = ......$
Question 82 :
The value of$ \displaystyle \tan 1^{\circ}\tan 2^{\circ}\tan 3^{\circ}.....\tan 89^{\circ} $ is
Question 83 :
The value of $\cos 1^{\circ}. \cos 2^{\circ}. \cos 3^{\circ} ...\cos 179^{\circ}$ is equal to:
Question 84 :
Express the trigonometric ratios $\sin A, \sec A$ and $\tan A$ in terms of $\cot A$
Question 87 :
If $\cos A+\cos^{2}A=1  $, then the value of $ \sin^2A+\sin^{4}A$ is:<br/>
Question 88 :
The value of ${ e }^{ \log _{ 10 }{ \tan { 1+ } } \log _{ 10 }{ \tan { 2+\log _{ 10 }{ \tan { 3+...+\log _{ 10 }{ \tan { 89 } } } } } } }$ is
Question 89 :
The value of$\displaystyle \frac { \tan { { 49 }^{ o } } }{ \cot { { 41 }^{ o } } }$ is :
Question 91 :
If $\displaystyle \sec \theta +\tan \theta=p$, then find the value of $\tan \theta$.<br/>
Question 95 :
If $\cos A = 0.6$, then the value of $5 \tan A - 4 \sec A$ is equal to 
Question 96 :
If $\sin { A } =a\cos { B } $ and $\cos { A } =b\sin { B } $, then $\left( { a }^{ 2 }-1 \right) \tan ^{ 2 }{ A } +\left( 1-{ b }^{ 2 } \right) \tan ^{ 2 }{ B } $   is equal to
Question 98 :
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 99 :
The value of $\displaystyle \sec { { 41 }^{ o } } \sin { { 49 }^{ o }+ } \cos { { 49 }^{ o } } \text{cosec }{ 41 }^{ o }$ is :
Question 100 :
If a.cot $\theta+$b.cosec $\theta = $ p and b.cot $\theta\ +\ $a.cosec $\theta =q$, then the value of $p^{2}-q^{2}$ is equal to:<br/>
Question 101 :
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 102 :
The function $f:\left [-\displaystyle \frac{1}{2},\:\displaystyle \frac{1}{2} \right ]\rightarrow \left [-\displaystyle \frac{\pi }{2},\:\displaystyle \frac{\pi}{2} \right ] $ defined by$ \sin^{-1}\left ( 3x-4x^{3} \right ) $ is
Question 104 :
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 105 :
The value of $ \cos y \cos\left(\dfrac{\pi}{2} -x\right) - \cos \left(\dfrac{\pi}{2}-y \right)\cos x + \sin y \cos\left(\dfrac{\pi}{2}-x\right)+ \cos x \sin\left(\dfrac{\pi}{2} -y\right)$ is zero if
Question 106 :
In a right angle triangle $\triangle ABC,\,\sin ^{ 2 }{ A } +\sin ^{ 2 }{ B } +\sin ^{ 2 }{ C } $ is
Question 107 :
If the angles of a triangle are in arithmetic progression such that $\sin (2A+B)=\dfrac{1}{2}$, then
Question 108 :
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$.
Question 110 :
In $\triangle ABC, \angle B = 90^{\circ}, BC = 7$ and $AC - AB = 1$, then $\cos C = .....$
Question 111 :
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 112 :
In atriangle $ABC$, $\sin A\cos B=\dfrac{1}{4}$ and $3\tan A=\tan B$ , the triangle is
Question 114 :
If $cosec \theta -\sin \theta =m$ and $\sec \theta -\cos \theta =n$, eliminate $\theta $.<br><br>
Question 115 :
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 116 :
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 117 :
If $\displaystyle \frac{x}{a}\cos \theta +\frac{y}{b}\sin \theta =1,\frac{x}{a}\sin \theta-\frac{y}{b}\cos \theta=1,$ then eliminate $\theta $<br>
Question 119 :
If $\sin x + \sin^{2}x=1,$ then the value of $\cos^{12} x + 3 \cos^{10} x + 3 cos^{8} x + cos ^{6} x -1$ is equal to :
Question 120 :
Which one of the following when simplified is not equal to one?
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 :
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 124 :
If $\text{cosec } \theta = \dfrac {13}{5}$, then $\cos \theta = ......$
Question 126 :
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 127 :
$1)$ 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 130 :
What is $\left(\dfrac{sec 18^{\circ}}{sec 144^{\circ}} + \dfrac{cosec 18^{\circ}}{cosec 144^{\circ}}\right)$ equals to?
Question 131 :
If $x \cos \alpha +y \sin \alpha=x \cos\beta+y \sin\beta=2a(0 < \alpha, \beta < \pi /2)$, then
Question 133 :
If $ \cos^{-1}\left ( 4x^{3}-3x \right )= 2\pi -3\cos^{-1}x $, then $ x $ lies in interval
Question 135 :
<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 136 :
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 137 :
If $2 \sec 2\alpha = \tan\beta + \cot \beta$, then one of the value of $\alpha+\beta$ is-
Question 140 :
If $\tan { \theta  } +\sin { \theta  } =m, \tan { \theta - \sin { \theta =n }  } $, then $(m^{2}-n^{2})^{2}=$.<br/>
Question 141 :
A person on the top of tower observes scooter moving with uniform velocity towards the base of the tower he finds that the angle of depression changes from$\displaystyle 30^{\circ}$ to$\displaystyle 60^{\circ}$ in 18 minutes The Scooter will reach the base of the tower in next
Question 144 :
If $\displaystyle X=\tan 1^{0}+\tan 2^{0}+........+\tan 45^{0}$ and $\displaystyle y= -(\cot 46^{0}+\cot 47^{0}+.......+\cot 89^{0})$ then find the value of $(x + y)$.
Question 145 :
If $\sin x= \cos y,\sqrt{6}\sin y= \tan z$ and $2\sin z= \sqrt{3}\cos x$; $u,v,w$ denotes respectively $\sin ^{2}x, \sin ^{2}y, \sin ^{2}z$ then the value of the triplet $\left ( u,v,w \right )$ is
Question 146 :
If $\sin A, \cos A$ and $\tan A$ are in G.P. then $\cot^6 A- \cot^2A$ is equal to
Question 148 :
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 149 :
If$\displaystyle \sin \Theta =\frac{3}{5} $ and$\displaystyle \Theta $ is acute then find the value of$\displaystyle \frac{\tan \Theta -2\cos \Theta }{3\sin \Theta +\sec \Theta }$
Question 150 :
${\cos ^2}{48^ \circ } - {\sin ^2}{12^ \circ }$ is equal to -
