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# Trig identity. cos2x/(1+sin2x)= tan(pi/4-x)?

Can someone help prove this? Steps would be appreciated.

cos2x/(1+sin2x)= tan(pi/4-x)

### 2 Answers

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- icemanLv 710 years agoFavorite Answer
LHS = cos2x / (1 + sin2x)

= (cos^2 x - sin^2 x) / (cos^2 x + sin^2 x + 2sin x cos x)

= [(cos x + sin x)(cos x - sin x)] / (cos x + sin x)^2

= (cos x - sin x) / (cos x + sin x) → divide each term by cos x

= (1 - tanx) / (1 + tan x)

= (tan π/4 - tan x) / (1 - tan π/4 tan x)

= tan (π/4 - x) = RHS

∎

- mexicanoLv 44 years ago
RHS = (tan pi/4 - tan x)/(one million+ tan x tan pi/4) = (one million-tan x)/(one million+an x) = (cos x -sin x)/(sin x+ cos x) = ( cos x- sin x)(sin x + cos x)/(sin x+ cos x)^2 = (cos ^2 x -sin ^2 x)/(sin ^2 x+ cos^2 x + 2 sin x cos x) = cos 2x/(one million+ sin 2x)

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