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

1 Answer
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)