Inverse Trigono...

If $$2\sinh ^{ -1 }{ \left( \dfrac { a }{ \sqrt { 1-{ a }^{ 2 } }  }  \right)  } =\log { \left( \dfrac { 1+x }{ 1-x }  \right)  }$$, then $$x=$$

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

Range of the function $$f(x)=4{ tan }^{ -1 }x+3{ sin }^{ -1 }x+{ sec }^{ -1 }x$$ is

If $$\sin \left( \sin^{-1} \dfrac{1}{5} +  \cos^{-1} x \right) = 1$$, then x is equal to

Number of solution of the equation $$\cos^{-1}(1-x)-2\cos^{-1}x=\dfrac{\pi}{2}$$ is 

If $$\sin ^{ -1 }{ \left( x-\displaystyle\frac { { x }^{ 2 } }{ 2 } +\displaystyle\frac { { x }^{ 3 } }{ 4 } -....\infty  \right)  } +\cos ^{ -1 }{ \left( { x }^{ 2 }-\displaystyle\frac { { x }^{ 4 } }{ 2 } +\displaystyle\frac { { x }^{ 6 } }{ 4 } -....\infty  \right)  } =\displaystyle\frac { \pi  }{ 2 } $$ and $$0<x<\sqrt { 2 } $$ then $$x$$ =

If $$ a sin^{-1} x -b cos^{-1}x =c$$, then the value of $$ a sin ^{-1} x + b cos^{-1} x$$ (whenever exists) is equal to

The set of values of $$'x'$$ for which the formula $$2 \sin^{-1}x=\sin^{-1} (2x\sqrt{1-x^{2}})$$ is true, is

If $$x=\cos^{ - 1}\left( \dfrac{2}{3} \right) + \tan^{ - 1}\left( \dfrac{1}{7} \right)$$ then $$x$$=

The  set for which $$2{\cos ^{ - 1}}x = {\cos ^{ - 1}}\left( {2{x^2} - 1} \right)$$ is valid is