Inverse Trigono...

$$\tan \left[\dfrac{\pi}{4} + \dfrac{1}{2} \cos^{-1} \left(\dfrac{5}{7} \right) \right] + \cot \left[\dfrac{\pi}{4} + \dfrac{1}{2} \cos^{-1} \left(\dfrac{5}{7}\right) \right]$$ is equal to 

$$\tan ^{ -1 }{ \sqrt { 3 }  } -\cot ^{ -1 }{ \left( -\sqrt { 3 }  \right)  } $$ is equal to

$${\cos ^{ - 1}}\left\{ {\dfrac{1}{{\sqrt 2 }}\left( {\cos \dfrac{{9\pi }}{{10}} - \sin \dfrac{{9\pi }}{{10}}} \right)} \right\} = $$

If $${ x }_{ 1 },{ x }_{ 2},{ x }_{ 3}$$ are positive roots of $$ x^{ 3 }-6x^{ 2 }+3px-2p=0\quad (p\in R)$$, then the value of $$\sin ^{ -1 } \left( \frac { 1 }{ { x }_{ 1 } } +\frac { 1 }{ { x }_{ 2 } }  \right) +\cos ^{ -1 }{ \left( \frac { 1 }{ { x }_{ 2 } } +\frac { 1 }{ { x }_{ 3 } }  \right)  } -\tan ^{ -1 }{ \left( \frac { 1 }{ { x }_{ 3 } } +\frac { 1 }{ { x }_{ 1 } }  \right)  } $$ is equal to

If $$\tan{\alpha}=\dfrac{m}{m+1}$$ and $$\tan{\beta}=\dfrac{1}{2m+1}$$ find the possible values of $$(\alpha+\beta)$$

$$\mathop {\lim }\limits_{n \to \infty } \sum\limits_{r = 1}^n {{{\tan }^{ - 1}}\left( {\dfrac{{2r}}{{1 - {r^2} + {r^4}}}} \right)} $$ is equal to 

Given that $$0 \le x\le \dfrac 12$$ the value of $$\tan \left[ { sin }^{ -1 }\left( \dfrac { x }{ \sqrt { 2 }  } +\sqrt { \dfrac { 1-{ x }^{ 2 } }{ 2 }  }  \right) -{ sin }^{ -1 }x \right]$$ is

The value of $$\sin^{-1}\left\{ \cot { \left\{ \sin ^{ -1 }{ \sqrt { \frac { 2-\sqrt { 3 }  }{ 4 }  } +\cos ^{  }{ \frac { \sqrt { 12 }  }{ 4 } +\sec ^{ -1 }{ \sqrt { 2 }  }  }  }  \right\}  }  \right\} $$ is equal to

the value of $$\cos ^{ -2 }{ \left( \cos { 10 }  \right)  }$$ is

The solution set of the equation $$\sin^{-1}\sqrt{1-x^2}+\cos^{-1}x=\cot^{-1}\dfrac{\sqrt{1-x^2}}{x}-\sin^{-1}x$$ is?