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Math Help - Verifying trig identities

  1. #1
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    Verifying trig identities

    Verify the identity: 2cos4xsin2x=2sin3xcos3x-2cosxsinx.

    I know I have to use the product to sum identities but im still stuck.
    So far I have, sin(3x+3x)+sin(3x-3x)-sin(x+x)-sin(x-x)
    What happens to the sin after you subtract 3x-3x and x-x?
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by kelsey3 View Post
    Verify the identity: 2cos4xsin2x=2sin3xcos3x-2cosxsinx.

    I know I have to use the product to sum identities but im still stuck.
    So far I have, sin(3x+3x)+sin(3x-3x)-sin(x+x)-sin(x-x)
    What happens to the sin after you subtract 3x-3x and x-x?
    Lets start with the right hand side

    \underbrace{2\sin(3x) \cos(3x)}_{=\sin(6x)} -2 \sin(x) \cos(x)

    \underbrace{\sin(6x)}_{\sin(2x)\cos(4x)+\sin(4x)\c  os(2x)} -2\sin(x)\cos(x)

    \sin(2x)\cos(4x)+\underbrace{\sin(4x)}_{2\sin(2x)\  cos(2x)}\cos(2x) -2\sin(x)\cos(x)

    \sin(2x)\cos(4x)+2\sin(2x) \underbrace{\cos^{2}(2x)}_{\frac{1+\cos(4x)}{2}} -\underbrace{2\sin(x)\cos(x)}_{\sin(2x)}

    \sin(2x)\cos(4x)+\sin(2x) +\sin(2x)\cos(4x)-\sin(2x)

    2 \sin(2x) \cos(4x)

    Yeah!!

    Im curious if there is a faster way? anyone?
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  3. #3
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    Think Soroban got it in the other, double-posted thread.
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