Inverse Trigono...

If $$f(x)=sin^{-1}(sinx)+cos^{-1}(sinx)$$ and $$\phi (x)=f(f(f(x))),$$ then $$\phi '(x)=$$ 

$$\tan^{-1}\dfrac {1}{5}+\tan^{-1}\dfrac {1}{7}+\tan^{-1}\dfrac {1}{3}+\tan^{-1}\dfrac {1}{8}$$ is equal to

If $$n - 1\sum\limits_{}^\infty  {{{\cot }^{ - 1}}\left( {{{{n^2}} \over 8}} \right) = \pi .} $$ where $${a \over b}$$ is rational number in its lowest, then correct option is/are 

If $$\sin (\sin^{-1}\dfrac{1}{5}+\cos ^{-1}x)=1$$, then find the value of x.

Find the value of :

The value of the expression $$2\sec^{-1} 2 +\sin^{-1} \dfrac{1}{2}$$ is 

Number of solutions of the equation $$3{\tan ^{ - 1}}x + {\cot ^{ - 1}}x = \pi $$ is

If $$x,y,z \in [-1,1]$$ such that $$\cos^{-1}x +\cos^{-1}y +\cos^{-1}z=0$$, find $$x+y+z$$.

Find the value of $$\sin^{-1}(2\cos^{2}x-1)+\cos^{-1}(1-2\sin^{2}x)$$.

Find the value of $$\cot (\tan^{-1} a +\cot^{-1} a)$$.