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Math Help - simplifying using half angle identity

  1. #1
    Junior Member
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    simplifying using double angle identity

    I think I got this right, but may be missing some steps or may be wrong entirely. The idea is to use the double angle identity to simplify

    sin4x

    = 2sin2xcos2x
    = 2(2sinxcosx)(1-2sin^2x)
    = 4sinxcosx(1-2sin^2x)
    = 4sinxcosx-8sin^3xcosx

    Is this right?
    Last edited by satis; March 10th 2010 at 04:53 PM.
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  2. #2
    Super Member bigwave's Avatar
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    Quote Originally Posted by satis View Post
    I think I got this right, but may be missing some steps or may be wrong entirely. The idea is to use the half angle identity to simplify

    sin4x

    = 2sin2xcos2x
    = 2(2sinxcosx)(1-2sin^2x)
    = 4sinxcosx(1-2sin^2x)
    = 4sinxcosx-8sin^3xcosx

    Is this right?
    not sure how you can really simplify just \sin{4x}

    also, the half angle formula is:

    \sin\left({\frac{\theta}{2}}\right) = \pm\sqrt{\frac{1-\cos{\theta}}{2}}
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  3. #3
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    that would be my mistake. I meant simplifying using the double angle formula. My apologies. Let's see if I can alter the thread title...yup!
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