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Math Help - Identities

  1. #1
    Member purplec16's Avatar
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    Identities

    Verify that the left side = the right side

    (sin t+cos t)^2= 1+ sin 2 t

    sin^2t + 2 sin t cos t+ cos^2 t = 1+ sin 2 t

     1+ 2sintcost= 1+ sin2t

    I cant seem to solve the identity
    Last edited by purplec16; March 17th 2010 at 06:36 AM. Reason: changed the question
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  2. #2
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    sin 2 t cos t
    This should be
    2sint cos t
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  3. #3
    Member purplec16's Avatar
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    Quote Originally Posted by sa-ri-ga-ma View Post
    sin 2 t cos t
    This should be
    2sint cos t
    I changed that, it was a typo
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  4. #4
    Member purplec16's Avatar
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    Quote Originally Posted by sa-ri-ga-ma View Post
    sin 2 t cos t
    This should be
    2sint cos t
    Do you know how to solve it from there?
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  5. #5
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    Quote Originally Posted by purplec16 View Post
    Do you know how to solve it from there?
    \sin(2t) = 2\sin{t}\cos{t} is the well known double angle identity.

    it comes from the sum identity for sine ...

    \sin(2t) = \sin(t+t) = \sin{t}\cos{t} + \cos{t}\sin{t} = 2\sin{t}\cos{t}
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