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Math Help - Double angle formulae

  1. #1
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    Double angle formulae

    Can someone please show me the process of answering this question?

    By writing sin3X as sin(2X+X), show that sin3X=3sinX−4sin^3X

    I know that sin2X=2sinXcosX and the other trig identities, but I cannot understand how to substitute it in, in particular the answer follows as:

    sin3X = sin2XcosX + cos2XsinX - it is this step that I am struggling with!

    Thanks
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  2. #2
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    Quote Originally Posted by CSG18 View Post
    Can someone please show me the process of answering this question?

    By writing sin3X as sin(2X+X), show that sin3X=3sinX−4sin^3X

    I know that sin2X=2sinXcosX and the other trig identities, but I cannot understand how to substitute it in, in particular the answer follows as:

    sin3X = sin2XcosX + cos2XsinX - it is this step that I am struggling with!

    Thanks
    Use the hint given at the start of the question and recall that \sin(A+B) = \sin A \cos B + \cos B \sin A

    \sin(2X+X) = \sin (2x) \cos (x) + \cos (2x) \sin(x)
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