Question

If tan x = 3 cot x then x = ?
(a) 60°
(b) 45°
(c) 30°
(d) 15°

Answer 1

Given: tanx = 3cotx


​$$\begin{gathered} \tan x=3\cot x \\ \Rightarrow \tan x=3\frac{1}{\tan x}\left(\because \cot x=\frac{1}{\tan x}\right) \\ \Rightarrow {\tan }^{2}x=3 \\ \Rightarrow \tan x=\sqrt{3} \\ \Rightarrow x=60°\left(\because \tan 60°=\sqrt{3}\right) \\ \mathrm{Hence},\mathrm{the}\mathrm{correct}\mathrm{option}\mathrm{is}\left(\mathrm{a}\right). \end{gathered}$$