How do you prove #(cosx-sinx)/(cosx+sinx)=(cos2x)/(1+sin2x)#?

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1 Answer
Nghi N.
Nov 26, 2015

Prove trig equation

Explanation:

#(cos x - sin x)/(cos x + sin x) =#
#= [(cos x - sin x)/(cos x + sin x)] [cos x + sin x)/(cos x + sin x)] =#
#=(cos^2 x - sin^2 x)/(cos x + sin x)^2 =#
Apply trig identities:
#cos^2 x - sin^2 x = cos 2x#
#(cos x + sin x)^2 = cos^2 x + 2sin x.cos x + sin^2 x = 1 + sin 2x#
Finally,
#(cos x - sin x)/(cos x + sin x) = (cos 2x)/(1 + sin 2x)#

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