Inverse Trigono...

$$\cot^{ -1 } 3 + \cot^{ -1 } 7 + \cot^{ -1 } 13 + n terms =$$

$$ \sin \cot ^{-1} \tan \cos ^{-1} x  $$ is always equal to

If $$\theta =\cot ^{ -1 }{ \sqrt { \cos { x }  } -\tan ^{ -1 }{ \sqrt { \cos { x }  }  }  } $$, then $$\sin { \theta  } =$$

$$3tan^{ -1 }x\quad =\quad tan^{ -1 }\{ \dfrac { 3x-x^{ 3 } }{ 1-3x^{ 2 } } \} ,\quad then\quad x\quad belong\quad to\quad $$

If $$\sin^{ -1 }\left(\dfrac { 2a }{ 1 + a^{ 2 } }\right) + \cos^{ -1 }\left(\dfrac { 1-a^{ 2 } }{ 1 + a^{ 2 } }\right) = \tan^{ -1 } \left(\dfrac { 2x }{ 1 x^{ 2 } }\right)$$ where, $$a, x \epsilon \left( 0, 1\right)$$ then the value of $$x$$ is

If $$\tan^{-1}{\left(\cfrac{\sqrt{1+x^2}-\sqrt{1-x^2}}{\sqrt{1+x^2}+\sqrt{1-x^2}}\right)}=\alpha,\left(\alpha\in\left[0,\cfrac{\pi}{4}\right)\right]$$ yhen $$x^2$$ is equal to

Value of $$\sin ^{ -1 }{ \frac { 3 }{ \sqrt { 13 }  } +\cos ^{ -1 }{ \frac { 11 }{ \sqrt { 146 }  }  } +\cot ^{ -1 }{ \sqrt { 3 }  }  } $$ is 

The least positive integer n for which $$\left( \frac { 1+i }{ 1-i }  \right) ^{ n }=\frac { 2 }{ \pi  } \left( \sec ^{ -1 }{ \frac { 1 }{ x } +\sin ^{ -1 }{ x }  }  \right) \left( where,\quad x\neq 0,-1\le x\ge 1\quad and\quad i=\sqrt { -1 }  \right) $$, is 

If $$2sin^{-1}( \frac {3}{5})-cos^{-1}(\frac{5}{13})=cos^{-1} (\lambda)$$, then $$\lambda$$ is eual to

If a is a real of the equation $${ x }^{ 3 }+3x-tan2=0$$ then $${ cot }^{ -1 }a+{ cot }^{ -1 }\dfrac { 1 }{ a } -\dfrac { x }{ 2 } $$ can be equal to