NIMCET 2017 — Mathematics PYQ

Concept:
${\cot }^{-1}(-x)=\pi -{\cot }^{-1}x$

Calculation:
${\cot }^{-1}(-\sqrt{3})=\pi -{\cot }^{-1}(\sqrt{3})$

Let, ${\cot }^{-1}(\sqrt{3})=\theta$

$\Rightarrow \cot \theta =\sqrt{3}$

$\Rightarrow \cot (\pi /6)=\sqrt{3}$

$\Rightarrow {\cot }^{-1}(\sqrt{3})=\frac{\pi }{6}$

${\cot }^{-1}(-\sqrt{3})=\pi -\frac{\pi }{6}$

$=\frac{5\pi }{6}$