Inverse Trigono...

$$\sum^ { \infty }_ { n=1 }   tan^{-1}\dfrac{4n}{n^4-2n^2+2}$$ is equal to:

$${ cos }^{ -1 }(\frac { x }{ 3 } )+{ cos }^{ -1 }(\frac { y }{ 2 } )=(\frac { \theta  }{ 2 } )$$ , then the value of $${ 4x }^{ 2 }$$-12xy cos$$(\frac { \theta  }{ 2 } )$$+$${ 9y }^{ 2 }$$ is equal to 

$$\cos ^{ -1 }{ \left\{ \dfrac { 1 }{ 2 } { x }^{ 2 }+\sqrt { { 1-x }^{ 2 } } .\sqrt { 1\dfrac { { x }^{ 2 } }{ 4 }  }  \right\}  } =\cos ^{ -1 }{ \dfrac { x }{ 2 }  } -\cos ^{ -1 }{ x } $$ holds for

$$tan^{-1}y=tan^{-1}x+tan^{-1}(\frac{2x}{1-x^{2}})$$ where $$|x| < \frac{1}{\sqrt{3}}$$. Then a value of y is:

$${ tanh }^{ -1 }\left( \frac { 1 }{ 3 }  \right) +{ coth }^{ -1 }\left( 3 \right) =.....$$

If $$x=si{ n }^{ -1 }(sin10)$$ and $$y={ s }^{ -1 }(cos10)$$ then $$y-x$$ is equal to:

$$\cos ^{ -1 }{ \left( \cos { \dfrac { 7\pi  }{ 6 }  }  \right)  } $$ is equal to

Evaluate $$\cot ^{ -1 }{ \sum _{ n=1 }^{ 19 }{ \cot ^{ -1 }{ [1+\sum _{ p=1 }^{ n }{ 2p } ] }  }  } $$

If $$x={ sin }^{ -1 }(sin10)$$ and $$y={ cos }^{ -1 }(cos10)$$, then the value of (y - x) is

The value of $$\sin^{-1}(\sin 3)+\cos^{-1}(\cos 7)-\tan^{-1}(\tan 5)$$ is