Mathematics - Inverse Trigonometric Functions Question with Solution | TestHub

For every real x, ${\tan }^{-1}x$ lies in (-$\pi /2,\pi /2$), so $\tan (|{\tan }^{-1}x|)=|x|$. Choice D is defined only for -1≤x≤1, and cannot be an identity over every real x. B fails for negative x, and C is not valid for arbitrary real x.