Inverse Trigono...

$$\displaystyle \tan^{-1}\left [ \cfrac{\cos\:x}{1+\sin\:x} \right ]$$ is equal to 

The value of $$\displaystyle tan(sin^{-1}(cos(sin^{-1}x)))tan(cos^{-1}(sin(cos^{-1}x)))$$, where $$x\:\epsilon\:(0,1)$$, is equal to 

The value of $$\displaystyle sin^{-1}(x^{2}-4x+6)+cos^{-1}(x^{2}-4x+6)$$ for all $$x\:\epsilon\:R$$ is

Which of the following is the solution set of the equation $$\displaystyle 2cos^{-1}x=cot^{-1}\left(\frac{2x^{2}-1}{2x\sqrt{1-x^{2}}}\right)$$

If $$\displaystyle \cos^{-1} x = a + \tan^{-1} \frac{\sqrt{1 - x^{b}}}{cx}$$ for $$\displaystyle x < 0$$.
Find the value of a ,b and c.

The equation $$\displaystyle 3cos^{-1}x-\pi\:x-\frac{\pi}{2}=0$$ has

$$\sin ^{ -1 }{ \left( \cos { \left( \sin ^{ -1 }{ x }  \right)  }  \right)  } +\cos ^{ -1 }{ \left( \sin { \left( \cos ^{ -1 }{ x }  \right)  }  \right)  } $$ is equal to

The number of real solution of the equation $$\displaystyle \sqrt{1+cos2x}=\sqrt{2}sin^{-1}(sin\:x),-\pi< x\leq \pi$$, is

There exists a positive real number $$x$$ satisfying $$\displaystyle \cos(\tan^{-1}x)=x$$. Then the value of $$\displaystyle \cos^{-1}\left(\frac{x^{2}}{2}\right)$$ is 

The value of $$\displaystyle \lim_{|x|\to\infty}cos(tan^{-1}(sin(tan^{-1}x)))$$ is equal to