Question 2 :
Solve:$\displaystyle \sin ^{4}\theta +2\cos ^{2}\theta \left ( 1-\frac{1}{\sec ^{2}\theta } \right )+\cos ^{4}\theta $

Question 4 :
The solution of $(2 cosx-1)(3+2 cosx)=0$ in the interval $0 \leq \theta \leq 2\pi$ is-

Question 5 :
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 8 :
Which of the following is equal to $\sin x \sec x$?

Question 9 :
Value of ${ cos }^{ 2 }{ 135 }^{ \circ  }$

Question 10 :
If $3\sin\theta + 5 \cos\theta =5$, then the value of $5\sin\theta -3 \cos\theta $ are 

Question 13 :
If $\tan \theta = \dfrac {4}{3}$ then $\cos \theta$ will be

Question 15 :
Given $\cos \theta = \dfrac{\sqrt3}{2}$, which of the following are the possible values of  $\sin 2 \theta$?

Question 16 :
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 18 :
Choose and write the correct alternative.<br>If $3 \sin \theta = 4 \cos \theta$ then $\cot \theta = ?$<br>

Question 19 :
Given $tan \theta =&#160;1$, which of the following is not equal to tan $\theta$?

Question 22 :
Calculate the value of $\sqrt {\dfrac {9\sin^{2} \theta + 9\cos^{2} \theta}{4}} $.

Question 23 :
If $\cos x= \tan y, \cot y = \tan z$ and $\cot z = \tan x$; then $\sin x = $

Question 24 :
If $\sin (\alpha+\beta)=1$ and $\sin(\alpha -\beta)=1/2$ where $\alpha, \beta \epsilon [0, \pi /2]$ then

Question 25 :
In $\triangle ABC, \angle B = 90^{\circ}, BC = 7$ and $AC - AB = 1$, then $\cos C = .....$

Question 26 :
If $3 \sin\theta+ 5 \cos\theta=5$, then $5 \sin\theta-3 \cos\theta$ is equal to<br/>

Question 27 :
If $a=\cos\alpha \cos\beta+\sin \alpha \sin\beta \cos\gamma$<br/>$b=\cos\alpha \sin \beta-\sin\alpha \cos\beta \cos\gamma$<br/>and $c=\sin \alpha \sin\gamma$, then $a^2+b^2+c^2$ is equal to

Question 28 :
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 29 :
${\cos ^2}{48^ \circ } - {\sin ^2}{12^ \circ }$ is equal to -

Question 30 :
If $\sin A, \cos A$ and $\tan A$ are in G.P. then $\cot^6 A- \cot^2A$ is equal to

Question 31 :
If $ \cos^{-1}\left ( 4x^{3}-3x \right )= 2\pi -3\cos^{-1}x $, then $ x $ lies in interval

Question 32 :
If$\displaystyle \sin \Theta =\frac{3}{5} $ and$\displaystyle \Theta $ is acute then find the value of$\displaystyle \frac{\tan \Theta -2\cos \Theta }{3\sin \Theta +\sec \Theta }$