Question 1 :
If $3\sin\theta + 5 \cos\theta =5$, then the value of $5\sin\theta -3 \cos\theta $ are 
Question 2 :
Given $\cos \theta = \dfrac{\sqrt3}{2}$, which of the following are the possible values of  $\sin 2 \theta$?
Question 3 :
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 5 :
Solve : $\dfrac { 2tan{ 30 }^{ \circ  } }{ 1+{ tan }^{ 2 }{ 30 }^{ \circ  } } $
Question 6 :
If $\sec 4A = cosec (A-20^{\small\circ})$, where $4A$ is an acute angle, find the value of $A$.
Question 8 :
Assertion: Statement 1: If $A,B,C$ are the angles of a triangle such that angle $A$ is obtuse,then $\displaystyle \tan B\tan C> 1$
Reason: Statement 2: In any triangle, $\displaystyle \tan A= \frac{\tan B+\tan C}{\tan B \tan C-1}$
Question 9 :
If $\left( 1+\tan { \theta } \right) \left( 1+\tan { \phi } \right) =2$, then $\left( \theta +\phi \right) $ is equal to
Question 12 :
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 13 :
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 14 :
If $16\cot \theta = 12$, then $\dfrac {\sin \theta - \cos \theta}{\sin \theta + \cos \theta} = $ _____
Question 15 :
If $ \cos^{-1}\left ( 4x^{3}-3x \right )= 2\pi -3\cos^{-1}x $, then $ x $ lies in interval
Question 18 :
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 19 :
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 20 :
For all real values of $\theta$ , $\cot\theta-2 \cot 2\theta$ is equal to
