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Question

Question: \[\cot x - \tan x =\]...

cot⁡x−tan⁡x=\cot x - \tan x =

A

cot⁡2x\cot 2x

B

2cot⁡2x2\cot^{2}x

C

2cot⁡2x2\cot 2x

D

cot⁡22x\cot^{2}{}2x

Answer

2cot⁡2x2\cot 2x

Explanation

Solution

cot⁡x−tan⁡x=cos⁡xsin⁡x−sin⁡xcos⁡x=cos⁡2x−sin⁡2xsin⁡xcos⁡x\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}

=2cos⁡2xsin⁡2x=2cot⁡2x.= \frac{2\cos 2x}{\sin 2x} = 2\cot{}2x.