Question 1 :
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 2 :
Given $tan \theta = 1$, which of the following is not equal to tan $\theta$?

Question 5 :
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 8 :
IF A+B+C=$ \displaystyle 180^{\circ}  $ ,then $  tan A+tanB+tanC $ is equal to

Question 9 :
Given $\cos \theta = \dfrac{\sqrt3}{2}$, which of the following are the possible values of  $\sin 2 \theta$?

Question 11 :
Find the value of $\displaystyle \cos { \left( { 90 }^{ o }-A \right)  } \tan { \left( { 90 }^{ o }-A \right)  } \sec { \left( { 90 }^{ o }-A \right)  } $

Question 12 :
The value of$\displaystyle \frac { \cos { \left( { 90 }^{ o }-A \right) } }{ 1+\sin { \left( { 90 }^{ o }-A \right) } } +\frac { 1+\sin { \left( { 90 }^{ o }-A \right) } }{ \cos { \left( { 90 }^{ o }-A \right) } }$ is equal to :

Question 13 :
Evaluate: $\displaystyle\frac{-\tan\theta \cot(90^o-\theta)+\sec\theta cosec(90^o-\theta)+\sin^235^o+\sin^255^o}{\tan 10^o\tan 20^o\tan 30^o \tan 70^o \tan 80^o}$.

Question 14 :
If $\alpha \in Q_3$ and $\tan\alpha =2$ then $\sin \alpha =$________.

Question 16 :
The value of$\displaystyle \frac { \cot { { 50 }^{ o } } }{ \tan { { 40 }^{ o } } }$ is :

Question 17 :
If $\displaystyle x=r\sin \theta \cdot \cos \phi,$  $y=r\sin \theta \cdot \sin \phi$ and $\displaystyle z= r\cos \theta$, then the value of $\displaystyle x^{2}+y^{2}+z^{2}$ is independent of 

Question 19 :
Which of the following is equivalent to $\dfrac {\tan n\,\, \text{cosec}\, n}{\sin n \,\,\sec n}$?

Question 20 :
The value of$ \displaystyle \frac{\cot \Theta + cosec \Theta -1}{\cot \Theta -cosec\Theta +1} $ is

Question 21 :
The value of $\cot 1^{\circ} \cot 2^{\circ} .... \cot 89^{\circ}$ is .....

Question 25 :
If $\displaystyle \sin \left ( A+B \right ) =\frac{\sqrt{3}}{2}$ and $\displaystyle \cot \left ( A-B \right )=1$, then find $A$

Question 26 :
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 27 :
If $ \sqrt3 \cos \theta + \sin \theta = \sqrt2 , $ then the most general value of $ \theta $ is :

Question 28 :
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 30 :
Solve : $4\sin x \cos x + 2 \sin x + 2 \cos x + 1 = 0$

Question 31 :
$1)$ 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 32 :
If $x \cos \alpha +y \sin&#160;\alpha=x \cos\beta+y \sin\beta=2a(0 &lt;&#160;\alpha, \beta &lt; \pi /2)$, then

Question 33 :
If $\sin {x}+\sin^{2}{x}+\sin^{3}{x}=1 ,\ \ then \ \ &#160;\cos^{6}{x}-4\cos^{4}{x}<br/>+8\cos^{2}{x}$ is equal to<br/>

Question 34 :
For all real values of $\theta$ , $\cot\theta-2 \cot 2\theta$ is equal to

Question 35 :
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