Question

find the value of Cot(Π/2-2cot^-1 √3)

Answer 1

$$\begin{gathered} \cot \left(\frac{\mathrm{\pi }}{2}-2{\cot }^{-1}\sqrt{3}\right) \\ =\tan \left(2{\cot }^{-1}\sqrt{3}\right) \\ \mathrm{Let}2{\cot }^{-1}\sqrt{3}=2\mathrm{x}\mathrm{such}\mathrm{that}\tan \left(2{\cot }^{-1}\sqrt{3}\right)=\tan 2\mathrm{x} \\ \mathrm{cotx}=\sqrt{3} \\ \mathrm{tanx}=\frac{1}{\sqrt{3}}=\tan \left(\frac{\mathrm{\pi }}{6}\right) \\ \mathrm{So}\mathrm{x}=\frac{\mathrm{\pi }}{6} \\ \mathrm{Now}\mathrm{subtituting}\mathrm{back}\mathrm{we}\mathrm{get}, \\ \tan \left(2{\cot }^{-1}\sqrt{3}\right)=\tan 2\mathrm{x}=\tan \left(\frac{\mathrm{\pi }}{3}\right)=\sqrt{3} \end{gathered}$$