Inverse Trigono...

If $$\theta\equiv sin^{-1}x+cos^{-1}x-tan^{-1}x,\ 0\leq x\leq 1$$, then the smallest interval in which $$\theta$$ lies is given by ?

The value of sin $$\sin \left\{ {{{\tan }^{ - 1}}\left( {\tan \frac{{7\pi }}{6}}

\right) + {{\cos }^{ - 1}}\left( {\cos \frac{{7\pi }}{3}} \right)}

\right\}$$ is

If $$\alpha \epsilon \left ( 0,\dfrac{\pi}{2}\right )$$, then the value of $$\tan ^{-1}(\cot \alpha )-\cot ^{-1}(\tan \alpha )+\sin ^{-1}(\sin \alpha )-\cos ^{-1}(\cos \alpha )$$ is equal to

If $$\tan ^{-1}\dfrac{\sqrt{1+x^{2}}-1}{x}=4^{\circ}$$,then

If $${\cot ^{ - 1}}x + {\cot ^{ - 1}}y + {\cot ^{ - 1}}z = \dfrac{\pi }{2}$$  then $$x+y+z$$ equals

If $$sin\left\{ \sin ^{ -1 }{ \cfrac { 1 }{ 5 }  } +\cos ^{ -1 }{ x }  \right\} =1$$, then $$x$$ is equal to

If $$0\le x\le 1$$, then $$\tan { \left\{ \cfrac { 1 }{ 2 } \sin ^{ -1 }{ \cfrac { 2x }{ 1+{ x }^{ 2 } } +\cfrac { 1 }{ 2 } \cos ^{ -1 }{ \cfrac { 2x }{ 1+{ x }^{ 2 } }  }  }  \right\}  } $$

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

If $$\displaystyle x$$ takes negative permissible value, then $$\displaystyle \sin ^{-1}x$$ is equal to

$$\sec ^{ 2 }{ \left( \tan ^{ -1 }{ 2 }  \right) +cosec ^{ 2 }{ \left( \cot ^{ -1 }{ 3 }  \right)  }  } $$=