Mathematics - Inverse Trigonometric Functions Question with Solution | TestHub

Use principal branches of ${\tan }^{-1},{\sin }^{-1}$ and ${\cos }^{-1}$. For $\mathrm{x}>1$, ${\tan }^{-1}\left(2\mathrm{x}/\left(1-{\mathrm{x}}^2\right)\right)=2{\tan }^{-1}\mathrm{x}-\pi$; for $|x|\le 1,{\sin }^{-1}\left(2x/\left(1+x^2\right)\right)=2{\tan }^{-1}x$. Also ${\sin }^{-1}u+{\cos }^{-1}u=\pi /2$ on $[-1,1]$.