Question

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

Answer 1

(b) 60^o

$$\begin{gathered} \tan x=3cotx \\ \Rightarrow \frac{\tan x}{\cot x}=3 \\ \Rightarrow {\tan }^{2}x=3\left[\because \cot x={\displaystyle \frac{1}{\tan x}}\right] \\ \Rightarrow \tan x=\sqrt{3}=\tan {60}^{\mathrm{o}} \\ \Rightarrow x={60}^o \end{gathered}$$