Question

Prove the following trigonometric identities.

sin² A cos² B − cos² A sin² B = sin² A − sin² B

Answer 1

We know that `sin^2 A + cos^2 A = 1`

So have

`sin^2 A cos^2 B - cos^2 A sin^2 B = sin^2 A (1 - sin^2 B) - (1 - sin^2 A) sin^2 B`

`= sin^2 A - sin^2 A sin^2 B - sin^2 B + sin^2 A sin^2 B`

`= sin^2 A - sin^2 B`

Hence proved.