use a double angle formula to rewrite the expression 4sin^2x-2

Question

please help with this problem i have an exam tomorrow

Answer 1

Lily

cos (x+y) = cos x cos y - sin x sin y

so cos 2x = cos ²x - sin ² x (setting y=x)

sin ²x + cos²x = 1

So cos² x = 1 - sin² x

so cos 2x = 1-2 sin ²x

So 2 sin ² x = 1- cos 2x

Nearly there !

You have 4 sin² x - 2, = 2 (1-cos 2x) - 2 = -2 cos 2x. Finished.

Mike