Q. The value of $\frac{\cot{x - \tan x}}{\cot{2x}}$ is
A) 1
B) 2
C) $- 1$
D) 4
Explanation
(b)
$\frac{\cot{x - \tan x}}{\cot{2x}}$
$= \tan{2x\left( \cot{x - \frac{1}{\cot x}} \right)}$
$= \tan{2x\left( \frac{\cot^{2}{x - 1}}{\cot x} \right)}$
$= \tan{2x\left( \frac{\cot^{2}{x - 1}}{2\cot x} \right)}.2$
$= \tan{2x.\cot{2x.2}}$
$= 2$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.