Calc

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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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