Question

Wnte the value of $\cos \left(\frac{{\tan }^{-1}x+{\cot }^{-1}x}{3}\right),\mathrm{when}x=-\frac{1}{\sqrt{3}}$

Answer 1

$$\begin{gathered} \cos \left(\frac{{\tan }^{-1}x+{\cot }^{-1}x}{3}\right)=\cos \left(\frac{\mathrm{\pi }}{6}\right)\left[\because {\tan }^{-1}x+{\cot }^{-1}x=\frac{\mathrm{\pi }}{2}\right] \\ =\frac{\sqrt{3}}{2} \end{gathered}$$