Inverse Trigono...

The range of $$ f\left( x \right) =\sin { =^{ -1 }x+ } \cos { =^{ -1 } } x+\tan { ^{ -1 } } x$$ is ?

The value of $$\sin ^{ -1 }{ \left[ \cot { \left( \sin ^{ -1 }{ \sqrt { \frac { 2-\sqrt { 3 }  }{ 4 }  }  } +\cos ^{ -1 }{ \frac { \sqrt { 2 }  }{ 4 } +\sec ^{ -1 }{ \sqrt { 2 }  }  }  \right)  }  \right]  } $$ is equal to

The value of $$\tan { \left\{ 4\tan { ^{ -1 }\left( \dfrac { 1 }{ 5 }  \right) -\tan { ^{ -1 }\left( \dfrac { 1 }{ 239 }  \right)  }  }  \right\}  }$$ is

The exhaustive set of values of $$'a'$$ such that $$x^{2}+ax+sing^{-1}\ (x^{2}-4x+5)+\ cos^{-1}(x^{2}-4x+5)=0$$ has at least one solution is

If $$\left |{\cos ^{ - 1}}\left( {\dfrac{{1 - {x^2}}}{{1 + {x^2}}}} \right)\right |\,\, < \,\dfrac{\pi }{3},\,then\,:$$ 

$$\sin^{-1}\left(a-\dfrac{a^2}{3}+\dfrac{a^3}{9}+...\right)+\cos^{-1}(1+b+b^2+...)=\dfrac{\pi}{2}$$ when?

If $$y=\cos^{-1}{\cos{4}}$$, then $$y=$$

$$3\cot^{-1}{\left(\dfrac{1}{2+\sqrt{3}}\right)}-\cot^{-1}\left(\dfrac{1}{x}\right)=\cot^{-1}\left(\dfrac{1}{3}\right)+\dfrac{\pi}{2}$$ then $$x=$$?

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

$$cos({ cos }^{ -1 }cos(\frac { 8\pi  }{ 7 } )+{ tan }^{ -1 }tan(\frac { 8\pi  }{ 7 } ))$$ has the value equal to -