Question 3 :
If $ABCD$ is a cyclic quadrilateral such that $12$ $\tan A-5=0$ and 5 $\cos B+3=0$, then $\cos C\tan D=$<br/>

Question 4 :
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 5 :
$\cos { { 1 }^{ o } } .\cos { { 2 }^{ o } } .\cos { { 3 }^{ o } } ......\cos { { 179 }^{ o } } $ is equal to

Question 6 :
Find the relation obtained by eliminating$\displaystyle \theta $ from the equation$\displaystyle x=a\cos \theta +b\sin \theta $ and$\displaystyle y=a\sin \theta -b\cos \theta $

Question 7 :
If$\displaystyle \cos \theta =\frac{3}{5},$ then the value of$\displaystyle \frac{\sin \theta -\tan \theta +1}{2\tan ^{2}\theta }$

Question 8 :
If $2 \sec 2\alpha = \tan\beta + \cot \beta$, then one of the value of $\alpha+\beta$ is-

Question 10 :
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 11 :
${\cos ^2}{48^ \circ } - {\sin ^2}{12^ \circ }$ is equal to -

Question 13 :
If the quadratic equation $ax^2+bx+c=0$ ($a &gt; 0$) has $\sec^2\theta$ and $\text{cosec}^2\theta$ as its roots, then which of the following must hold good?<br>

Question 15 :
Let $\displaystyle -\frac { \pi }{ 6 } &lt;\theta &lt;-\frac { \pi }{ 12 }$, 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$\displaystyle { \alpha }_{ 1 }&gt;{ \beta }_{ 1 }$ and$\displaystyle { \alpha }_{ 2 }&gt;{ \beta }_{ 2 }$, then$\displaystyle { \alpha }_{ 1 }+{ \beta }_{ 2 }$ equals to

Question 16 :
The value of the expression $\displaystyle 1\, - \,\frac{{{{\sin }^2}y}}{{1\, + \cos \,y}}\, + \frac{{1\, + \cos \,y}}{{\sin \,y}}\, - \,\frac{{\sin \,y}}{{1\, - \cos \,y}}$ is equal to&#160;

Question 17 :
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 18 :
What is $\left(\dfrac{sec 18^{\circ}}{sec 144^{\circ}} + \dfrac{cosec 18^{\circ}}{cosec 144^{\circ}}\right)$ equals to?

Question 20 :
If $\sin A, \cos A$ and $\tan A$ are in G.P. then $\cot^6 A- \cot^2A$ is equal to

Question 22 :
If $x = a \cos^{3} \theta \sin^{2} \theta, y = a \sin^{3} \theta \cos^{2} \theta$ and $\dfrac {(x^{2} + y^{2})^{p}}{(xy)^{q}}(p, q\epsilon N)$ is independent of $\theta$, then

Question 23 :
If $\sin\theta + \sin^{2}\theta = 1$, then $\cos^{2}\theta + \cos^{4}\theta = ......$

Question 24 :
If $\cos x= \tan y, \cot y = \tan z$ and $\cot z = \tan x$; then $\sin x = $

Question 26 :
If $ \cos^{-1}\left ( 4x^{3}-3x \right )= 2\pi -3\cos^{-1}x $, then $ x $ lies in interval

Question 28 :
The value of the expression $(\tan1^{0} \tan2^{0} \tan 3^{0}...\tan89^{0})$ is equal to<br/>

Question 30 :
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 31 :
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 32 :
Which one of the following when simplified is not equal to one?

Question 34 :
If the angles of a triangle are in arithmetic progression such that $\sin (2A+B)=\dfrac{1}{2}$, then

Question 35 :
If $\text{cosec } \theta = \dfrac {13}{5}$, then $\cos \theta = ......$

Question 36 :
<br/>Given that $\sec\theta+\tan\theta=1$ then one root of the equation $(a-2b+c)x^{2}+(b-2c+a)x+(c-2a+b)= 0$ is<br/>

Question 37 :
If $5\cos { A } =4\sin { A } $, then $\tan { A=\_ \_ \_ } $

Question 39 :
$1)$ 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 40 :
If $\sin (\alpha+\beta)=1$ and $\sin(\alpha -\beta)=1/2$ where $\alpha, \beta \epsilon [0, \pi /2]$ then

Question 42 :
For all real values of $\theta$ , $\cot\theta-2 \cot 2\theta$ is equal to

Question 43 :
In atriangle $ABC$, $\sin A\cos B=\dfrac{1}{4}$ and $3\tan A=\tan B$ , the triangle is

Question 45 :
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 46 :
In a triangle $ABC$, right angled at $C$, $a$, $b$&#160;$c$&#160;are the lengths of&#160;sides of triangle and hypotenuse respectively. Find the value of&#160;$\tan A+\tan B$.

Question 47 :
If $cosec \theta -\sin \theta =m$ and $\sec \theta -\cos \theta =n$, eliminate $\theta $.<br><br>

Question 49 :
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 50 :
If $\displaystyle&#160;\frac { \sin { \alpha &#160;} &#160;}{ \sin { \beta &#160;} &#160;} =\frac { \sqrt { 3 } &#160;}{ 2 } $ and $\displaystyle&#160;\frac { \cos { \alpha &#160;} &#160;}{ \cos { \beta &#160;} &#160;} =\frac { \sqrt { 5 } &#160;}{ 2 } ,0&lt;\alpha ,\beta &lt;\frac { \pi &#160;}{ 2 } $, then