# Calc

posted by .

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

• Calc -

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

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