Calc
posted by Chris on .
Which expression is equivalent to sin(3x) + sin x?
A.
2cos(2x)sin x
B.
2sin(2x)sin x
C.
2sin(2x)cos x
D.
2sin(2x)cos x
E.
2cos(2x)sin x

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