This as far as I get to making the left side the same as the right. I could use the steps I am missing

$\displaystyle sin\, 3x = sin(x+2x)$

$\displaystyle = sin\, x \cos 2x + \cos x \sin 2x$

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

but I get lost from here to get the left and right sides the same.

thank you!