Help proving please?

Not even sure where to start here... This book went from 0-1000 mph in a heartbeat.

I need to prove:

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

1 Answer
May 6, 2018

Refer explanation.

Explanation:

To prove #(cos x + sin x)^2 - sin (2x) = 1#

First, remove the brackets.

#=> cos x^2 + 2 sin x cos x + sin x^2 - sin (2x)#

Apply #sin (2x) = 2 sin x cos x#

#=> cos x^2 +cancel(2 sin x cos x) -cancel (2 sin x cos x) + sin x^2#

Apply #sin x^2 + cos x^2 = 1#

#:. cos x^2 + sin x^2 = 1 sqrt# Proven