Inverse Trigono...

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

The smallest and largest value of $$\tan^{-1}\left(\dfrac {1-x}{1+x}\right),0 \le x \le 1$$ are

$$ \sin ^{-1}\left(\dfrac{1}{\sqrt{2}}\right)+\sin ^{-1}\left(\dfrac{\sqrt{2}-1}{\sqrt{6}}\right)+\ldots+\sin ^{-1}\left(\dfrac{\sqrt{n}-\sqrt{n-1}}{\sqrt{n(n+1)}}\right)+\ldots . \infty= $$

If  $$\cot  \dfrac { 2{ x } }{ 3 } +\tan  \dfrac { { x } }{ 3 } =\csc  \dfrac { { kx } }{ 3 } ,$$  then the value of  $$\tan ^{ { -1 } } (\tan { k } )$$  equals

The value of the expression tan$$(\frac{1}{2} cos ^{-1}\frac{2}{\sqrt{5}})$$ is

$$4\tan ^{ -1 }{ \frac { 1 }{ 5 }  } -\tan ^{ -1 }{ \frac { 1 }{ 70 }  } +\tan ^{ -1 }{ \frac { 1 }{ 99 }  } =$$

Considering only the principal values of inverse functions, the set $$A=\left\{ x\quad \ge \quad 0\quad :tan^{ -1 }(2x)+tan^{ -1 }(3x)=\dfrac { \pi  }{ 4 }  \right\} $$

The value of $$\sin ^{ -1 }{ (\cos { (\cos ^{ -1 }{ (\cos { x } ) } +\sin ^{ -1 }{ (\sin { x } ) } ) } ) } ,\quad where\quad x\in (\frac { \pi  }{ 2 } ,\pi )$$, is equal to 

The value of $$\sin^{-1}(\sin 12)-\cos^{-1}(\cos 12)=$$

$$\tan ^{ -1 }{ (\frac { 5 }{ 12 } ) } +\sin ^{ -1 }{ (\frac { 24 }{ 25 } ) } =\cos ^{ -1 }{ (x) } \Rightarrow x=$$