Question 1 :
$$\quad \sin ^{ -1 }{ x } +\sin ^{ -1 }{ \cfrac { 1 }{ x } } +\cos ^{ -1 }{ x } +\cos ^{ -1 }{ \cfrac { 1 }{ x } = } $$

Question 2 :
Consider $$x = 4\tan^{-1}\left (\dfrac {1}{5}\right ), y = \tan^{-1} \left (\dfrac {1}{70}\right )$$ and $$z = \tan^{-1}\left (\dfrac {1}{99}\right )$$.What is $$x$$ equal to?

Question 3 :
The value of $$\cos^{-1} (\cos 12) - \sin^{-1} (\sin 12)$$ is 

Question 4 :
$$\sin ^ { - 1 } 5 + \cos ^ { - 1 } 5 = \ldots \ldots$$

Question 5 :
Simplify $${\cot ^{ - 1}}\dfrac{1}{{\sqrt {{x^2} - 1} }}$$ for $$x <  - 1$$

Question 7 :
Solve $${\cos ^{ - 1}}\left( {\frac{4}{5}} \right) + {\cos ^{ - 1}}\left( {\frac{{63}}{{65}}} \right) = $$

Question 8 :
The value of $$\sin^{-1} \left( \dfrac{2 \sqrt 2}{3} \right ) + \sin^{-1} \left( \dfrac{1}{3}\right )$$ is equal to

Question 11 :
Consider the following statements:<br/>1. $$\tan^{-1} 1+ \tan^{-1} (0.5) = \dfrac {\pi}2$$<br/>2.&#160;$$\sin^{-1}{\cfrac{1}{3} }+ \cos^{-1}{\cfrac{1}{3}} =\cfrac{\pi}{2}$$<br/>Which of the above statements is/are correct ?&#160;

Question 12 :
$${ tan }^{ -1 }x+{ tan }^{ -1 }y={ tan }^{ -1 }\dfrac { x+y }{ 1-xy } $$,&#160; &#160; &#160; $$xy&lt;1$$<br/>&#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; $$=\pi +{ tan }^{ -1 }\dfrac { x+y }{ 1-xy } $$,&#160; &#160; &#160; $$xy&gt;1$$.<br/>&#160;Evaluate:&#160; $${ tan }^{ -1 }\dfrac { 3sin2\alpha&#160; }{ 5+3cos2\alpha&#160; } +{ tan }^{ -1 }\left( \dfrac { tan\alpha&#160; }{ 4 }&#160; \right) $$<br/>&#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; where $$-\dfrac { \pi&#160; }{ 2 } &lt;\alpha &lt;\dfrac { \pi&#160; }{ 2 } $$

Question 14 :
The number of real values of x satisfying the equation $$\tan^{-1}\left(\dfrac{x}{1-x^2}\right)+\tan^{-1}\left(\dfrac{1}{x^3}\right)=\dfrac{3\pi}{4}$$, is?

Question 16 :
Solve:$$\displaystyle \sin { \left( { \tan }^{ -1 }x \right) } ,\left| x \right| &lt;1$$ is equal to

Question 18 :
Calculate the value of $$\displaystyle \sin^{-1} \cos \left ( \sin^{-1} x\right ) + \cos^{-1} \sin \left ( \cos^{-1} x \right ) $$. where $$\displaystyle\left | x \right | \leq 1$$

Question 20 :
Solve $$\cos { \left[ \tan ^{ -1 }{ \left[ \sin { \left( \cot ^{ -1 }{ x } &#160;\right) &#160;} &#160;\right] &#160;} &#160;\right] &#160;} $$

Question 21 :
The number of solutions for the equation $$2\sin ^{ -1 }{ \sqrt { { x }^{ 2 }-x+1 } &#160;} +\cos ^{ -1 }{ \sqrt { { x }^{ 2 }-x } &#160;} =\dfrac { 3\pi }{ 2 } $$ is

Question 22 :
The value of $$\tan { \left[ \dfrac { 1 }{ 2 } \cos ^{ -1 }{ \left( \dfrac { 2 }{ 3 } \right) } \right] } $$ is

Question 23 :
The value of $$ \cos \left( \sin^{-1} \left( \dfrac {2}{3} \right) \right) $$ is equal to :

Question 24 :
The value of $$\sin ^{ -1 }{ \left( \cos { \cfrac { 53\pi }{ 5 } } \right) } $$ is

Question 25 :
Consider the following :<br>1. $${\sin}^{-1}\dfrac{4}{5}+{\sin}^{-1}\dfrac{3}{5}=\dfrac{\pi}{2}$$<br>2. $${\tan}^{-1}\sqrt{3}+{\tan}^{-1}1=-{\tan}^{-1}(2+\sqrt{3})$$<br>Which of the above is/are correct?

Question 26 :
What is $$\sin { \left[ \sin ^{ -1 }{ \left( \cfrac { 3 }{ 5 } \right) } +\sin ^{ -1 }{ \left( \cfrac { 4 }{ 5 } \right) } \right] } $$ equal to?

Question 27 :
If $$\dfrac {(x + 1)^{2}}{x^{3} + x} = \dfrac {A}{x} + \dfrac {Bx + C}{x^{2} + 1}$$, then $$\csc^{-1}\left (\dfrac {1}{A}\right ) + \cot^{-1}\left (\dfrac {1}{B}\right ) + \sec^{-1}C =$$ ____

Question 29 :
$$ \sin \left( 2 \sin^{-1} \sqrt{\dfrac{63}{65}} \right) $$<br/>is equal to :

Question 30 :
If two angles of a triangle are $$\tan ^{ -1 }{ (2) } $$ and $$\tan ^{ -1 }{ (3) } $$, then the third angle is