I was doing an advance reading on trigonometry (identities, specifically) when I encountered these problems on verification:
sin 5x = 5 sin x - 20 sin^3 x + 16 sin ^ 5 y
sin 2x + sin 2y + sin 2z = 4 sin x sin y sin z
sin^2 x + sin ^2 (y-x) + 2 sin x cos y sin (y-x) = sin^2 y
I'll try to edit this when I come up with answers. Just tips or hints on what identities I should use will do. Thanks for those who will help!
... but anyway, back to your original question.
I'd prove the first one by using de Moivre's formula:
Substitute , multiply out the LHS, simplify out all the algebra (replacing every instance of with , then equating the real and imaginary parts.
If you haven't investigated complex numbers yet, then perhaps now would be a good time to get into them. Come on in, the water's lovely.