Inverse Trigono...

If $$\displaystyle { \left( \tan ^{ -1 }{ x }  \right)  }^{ 2 }+{ \left( \cot ^{ -1 }{ x }  \right)  }^{ 2 }=\frac { 5{ \pi  }^{ 2 } }{ 8 } $$, then $$x$$ equals

The value of p for which system has a solution is

$$\displaystyle ax+b(\sec(\tan^{-1}x))= c $$ and $$\displaystyle ay+b(\sec(\tan^{-1}y))= c $$, then the value of xy is,

The number of solution of the equation $$ 1+x^{2}+2x\:\sin \left ( \cos^{-1}y \right )= 0 $$ is :

If $$\displaystyle [cot^{-1}x]+[cos^{-1}x]=0$$, where $$[\cdot]$$ denotes the greatest integer function, then the complete set of values of $$x$$ is 

If $$ \sin^{-1}a +\sin^{-1}b+\sin^{-1}c= \displaystyle \frac{3\pi }{2} $$  and  $$ f\left ( 2 \right )=2,{f\left ( x+y \right )}= f\left ( x \right )\:f\left ( y \right )\:\:\forall \:\:x,\:y\:\epsilon \:R $$ then $$ a^{f\left ( 2 \right )}+\:b^{f\left ( 4 \right )}+\:c^{f\left ( 6 \right )}-\:\displaystyle \frac{3\left ( a^{f\left ( 2 \right )}. \:b^{f\left ( 4 \right )}.\:c^{f\left ( 6 \right )}\right )}{a^{f\left ( 2 \right )} +\:b^{f\left ( 4 \right )}+\:c^{f\left ( 6 \right )}} $$  equals

Find number of values of x which  satisfying $$\left [ \tan^{-1}x \right ]+\left [ \cot^{-1}x \right ]=2$$, where [.] represents the greatest integer function.

$$\displaystyle sin^{-1}(3x-2-x^{2})+cos^{-1}(x^{2}-4x+3)=\frac{\pi}{4}$$ can have a solution for $$x\:\epsilon$$

The number of solutions of $$\sin^{-1}\left ( 1+b+b^{2}+\cdots \infty \right )+\cos^{-1}\left ( a-\displaystyle\frac{a^{2}}{3}+\frac{a^{2}}{9}\cdots \infty  \right )= \displaystyle\frac{\pi }{2}$$ is

The number of integral values of $$k$$ for which the equation $$\displaystyle sin^{-1}x+tan^{-1}x=2k+1$$ has a solution is