Inverse Trigono...

The value of $$\sin \left(\dfrac {1}{4}\sin^{-1}\dfrac {\sqrt {63}}{8}\right)$$ is

If $$\sin ^{-1}x + \sin ^{-1}y + \sin ^{-1}z = \dfrac{3\pi}{2}$$, then $$(x^{500} + y^{500} + z^{500}) - (x^{501} + y^{501} + z^{501})$$ is

If $$\tan^{-1}\left(\dfrac{x+1}{x-1}\right)+\tan^{-1}\left(\dfrac{x-1}{x}\right)=\pi +\tan^{-1}(-7)$$, then $$x=$$

The number of real solutions of $$\cos ^ { - 1 } x + \cos ^ { - 1 } 2 x = - \pi$$ is

The value of $$ \sin (\cot^{-1}x)$$ is 

$$\cos ^ { - 1 } \left( \cos \left( \dfrac { - 17 \pi } { 5 } \right) \right)$$ is equal to

The value of $$\tan ^{-1} \left (\dfrac{1}{3}\right) +\tan ^{-1} \left (\dfrac{2}{9}\right) + \tan ^{-1}\left  (\dfrac{4}{33}\right) + \tan ^{-1} \left (\dfrac{8}{129}\right) +$$.......$$n$$ terms is

$$\sinh { \left( \cosh ^{ -1 }{ x }  \right)  } =$$

$$\sin\ h^{-1}{\left(2^{3/2}\right)}$$=

If $$\cot^{-1} [\sqrt{\cos \alpha}] - \tan^{-1} [\sqrt{\cos \alpha}] = x$$, then $$\sin x$$ is equal to