Question

Verify the identity.

cos (x - y) - cos (x + y) = 2 sin x sin y

Answer 1

I got that, what next?

Answer 2

trig identities for sum and difference:
cos (a + b) = cos a cos b - sin a sin b
cos (a - b) = cos a cos b + sin a sin b

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

Answer 3

That's it. I worked only on the left side, and I turned the left side into the right side, so the identity is proved.

Answer 4

Oh!

Answer 5

Thanks!

Answer 6

wlcm