Recall: sin (A + B) = sin A cos B + cos A sin B sin 2x = 2 sin x cos x cos 2x = cos^2 x - sin^2 x = 2 cos^2 x - 1 = 1 - 2 sin^2 x sin^2 x + cos^2 x = 1

sin 3x = sin (2x + x) = sin 2x. cos x + cos 2x. sin x = 2 sin x cos x. cos x + (1 - 2 sin^2 x) . sin x = 2 sin x cos x. cos x + sin x - 2 sin^3 x = 2 sin x cos^2 x + sin x - 2 sin^3 x = 2 sin x (1 - sin^2 x) + sin x - 2 sin^3 x = 2 sin x - 2 sin^3 x + sin x - 2 sin^3 x = 3 sin x - 4 sin^3 x.

I hope that helps. :)

May 6th, 2015

Studypool's Notebank makes it easy to buy and sell old notes, study guides, reviews, etc.