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Math Help - Trig

  1. #1
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    Trig

    prove the identity

    sin 3 x = 3 sin x - 4 sin ^3 x
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by meli3000 View Post
    prove the identity

    sin 3 x = 3 sin x - 4 sin ^3 x
    See this thread

    http://www.mathhelpforum.com/math-he...ease-help.html
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  3. #3
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    Hello, meli3000!


    Prove the identity: . \sin3x \:= \:3\sin x - 4\sin^3\!x
    We will need these identites:
    . . \sin(A+B) \;=\;\sin A\cos B + \sin B\cos A
    . . \sin2A \:=\: 2\sin A\cos A
    . . \cos2A \:=\:1-2\sin^2\!A
    . . \cos^2\!A \:=\:1 - \sin^2\!A


    \sin(3x) \;=\;\sin(2x + x)

    . . . . . = \;\sin(2x)\cos(x) + \sin(x)\cos(2x)

    . . . . . = \;(2\sin x\cos x)\cos x + \sin x(1 - 2\sin^2\!x)

    . . . . . = \;2\sin x\cos^2\!x + \sin x - 2\sin^3\!x

    . . . . . = \;2\sin x(1 - \sin^2\!x) + \sin x - 2\sin^3\!x

    . . . . . = \;2\sin x - 2\sin^3\!x + \sin x - 2\sin^3\!x

    . . . . . = \;3\sin x - 4\sin^3\!x

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