Posted by Chris on Thursday, April 18, 2013 at 11:42am.
I don't know if you came across the identity
sin (3x) = 3sinx - 4sin^3 x
so yours:
sin(3x) + sinx = 4sinx - 4sin^3 x
= 4sinx(1 - sin^2x)
= 4sinx(cos^2x)
= 2(2sinxcosx)(cox) --. I just grouped them
= 2(sin(2x) (cosx)
which is D