Inverse Trigono...

$$\tan (2\cos ^{-1}\frac 35)=$$_____

The solution set of the equation$$2 cos^{ -1 } x = cot^{ -1 } \left(\dfrac { 2x^{ 2 } - 1 }{ 2x \sqrt { 1 x^{ 2 } } }\right) $$ is

If $$\;\sin {\;^{ - 1}}\dfrac{1}{x} = 2\;{\tan ^{ - 1}}\dfrac{1}{7} + {\cos ^{ - 1}}\dfrac{3}{5}$$, then $$x =$$ ___

If $$\alpha =\cos^{-1}\left(\dfrac{3}{5}\right),\beta=\tan^{-1}\left(\dfrac{1}{3}\right)$$ where $$0<\alpha,beta <\dfrac{\pi}{2},$$then $$\alpha -\beta $$ is equal to :

If $$\cos ^{ -1 }{ x } -\cos ^{ -1 }{ \cfrac { y }{ 2 }  } =\alpha $$ where $$-1-1\le x\le 1,-2\le y\le 2,x\le \cfrac { y }{ 2 } $$ then for all $$4{ x }^{ 2 }-4xy\cos { \alpha  } +{ y }^{ 2 }$$ is equal to

The value of $$tan \left (\cos^{-1} \dfrac {3}{5} + \tan^{-1} \dfrac {1}{4}\right )$$ is

The value of $$\tan^{-1}\dfrac{1}{3}+\tan^{-1}\dfrac{1}{5}+\tan^{-1}\dfrac{1}{7}+\tan^{-1}\dfrac{1}{8}$$ is ___________.

$$\tan \left [2\tan^{-1}\dfrac {1}{5}-\dfrac {\pi}{4}\right]=$$ ?

$$\sin \left (\cos^{-1}\dfrac {3}{5}\right)=$$ ?

The value of $$\sin \left (\sin^{-1}\dfrac {1}{2}+\cos^{-1}\dfrac {1}{2}\right)=$$?