Question

Prove (sinxsiny-cosxcosy)(sinxsiny+cosxcosy) =sin^2x-cos^2y

Answer 1

Step-by-step explanation:

Recall that $\sin^2x + \cos^2x = 1$

$(\sin x \sin y - \cos x \cos y)(\sin x \sin y + \cos x \cos y)$

$= \sin^2 x \sin^2 y - \cos^2 x \cos^2 y$

$= \sin^2 x (1 - \cos^2 y) - \cos^2 x \cos^2 y$

$= \sin^2 x - \sin^2 x \cos^2y - \cos^2x \cos^2y$

$= \sin^2x - (\sin^2x + \cos^2x)\cos^2y$

$= \sin^2x - \cos^2y$