Question

The value of cot (tan^-1x + cot^-1x) for all x ∊ R, is ____________________

Answer 1

We know

${\tan }^{-1}x+{\cot }^{-1}x=\frac{\mathrm{\pi }}{2}$, for all x ∈ R

$\therefore \cot \left({\tan }^{-1}x+{\cot }^{-1}x\right)=\cot \frac{\mathrm{\pi }}{2}$

$\Rightarrow \cot \left({\tan }^{-1}x+{\cot }^{-1}x\right)=0$

The value of cot(tan⁻¹x + cot⁻¹x) for all x ∈ R, is __0__.