Will you prove this identity, please?

Question

(sinx - cosx)^2 = 1-sin2x

Answer 1

Hi,

Like the other one, distribute

(sinx - cosx)^2 = 1-sin2x

sin^2 x - 2 sin x cos x + cos^2 x = 1 - sin 2x

Now using the following identity
sin^2 x + cos^2 x = 1

We get
1 - 2 sin x cos x = 1 - sin 2x

Fortunately,
sin 2x = 2 sin x cos x

1 - sin 2x = 1 - sin 2x

QED

Hope that helps,
Matt

Answer 2

(sinx - cosx)^2 = 1-sin2x
sin^2x - 2sinxcosx +cos^2x = 1 - sin2x
1-2sinxcosx = 1-sin^2x
1-sin2x = 1-sin2x