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MCQ

$\cot x - \tan x = $

A
$\cot \,2x$
B
$2{\cot ^2}x$
✓
$2\,\,\cot \,2x$
D
${\cot ^2}\,2x$

✓

Answer

Correct option: C.

$2\,\,\cot \,2x$

c
(c) $\cot x - \tan x = \frac{{\cos x}}{{\sin x}} - \frac{{\sin x}}{{\cos x}} = \frac{{{{\cos }^2}x - {{\sin }^2}x}}{{\sin x\,\cos x}}$

$ = \frac{{2\,\cos \,2x}}{{\sin \,2x}} = 2\,\,\cot \,\,2x.$

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