Question

Express cot 2x in terms of cot x

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Answer 1

cot x = 2cot(2x) + tan x

Explanation:

`\rm \implies cot \: 2x = (cos \: 2x)/(sin \: 2x) \\ \\ \rm \implies cot \: 2x = \frac{ {cos}^(2)(x) - {sin}^(2)(x) }{2(sin \: x)(cos \: x)} \\ \\ \rm \implies cot \: 2x = (1)/(2) \bigg( (cos \: x)/(sin \: x) - (sin \: x)/(cos \: x) \bigg) \\ \\ \rm \implies cot \: 2x = (1)/(2) (cot \: x - tan \: x) \\ \\ \rm \implies 2cot ( 2x )= cot \: x - tan \: x \\ \\ \rm \implies cot \: x = 2cot (2x) + tan \: x`