Question

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

Answer 1

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