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Math Help - Stuck with trig identities

  1. #1
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    Stuck with 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
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    Hello, kelsey3!

    We need this double-angle identity: . 2\sin\theta\cos\theta \:=\:\sin2\theta

    And this sum-to-product identity: . \sin A - \sin B \:=\:2\cos\left(\frac{A+B}{2}\right)\sin\left(\fra  c{A-B}{2}\right)



    Verify the identity: .  2\cos4x\sin2x\;=\;2\sin3x\cos3x-2\cos x\sin x

    The right side is: . \underbrace{2\sin3x\cos3x} - \underbrace{2\sin x\cos x}

    . . . . . . . . . = \qquad\quad\underbrace{\sin6x \quad\;\;- \;\;\quad \sin 2x}

    . . . . . . . . . = \quad \overbrace{2\cos\left(\frac{6x+2x}{2}\right)\sin\l  eft(\frac{6x-2x}{2}\right)}

    . . . . . . . . . = \qquad\qquad\quad 2\cos4x\sin 2x

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  3. #3
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    Thank you sooo much!
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