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Math Help - trig identity

  1. #1
    Member pberardi's Avatar
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    trig identity

    Can someone tell me if this is correct
    sin(2t)cos(2t) = 1/4sin(4t)

    This is my reasoning
    sin(2t) = 2sin(t)cos(t) yes?
    sin(4t) = 4sin(t)cos(t) yes?
    therefore 1/4sin(4t) = sin(t)cos(t)
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by pberardi View Post
    Can someone tell me if this is correct
    sin(2t)cos(2t) = 1/4sin(4t)

    This is my reasoning
    sin(2t) = 2sin(t)cos(t) yes?
    sin(4t) = 4sin(t)cos(t) yes?
    therefore 1/4sin(4t) = sin(t)cos(t)
    You're almost there...but you're answer is incorrect.

    Note that \sin\left(2t\right)\cos\left(2t\right)\sim\sin\alp  ha\cos\alpha.

    From the double angle identity, 2\sin\alpha\cos\alpha=\sin\left(2\alpha\right). Thus, \sin\alpha\cos\alpha=\tfrac{1}{2}\sin\left(2\alpha  \right).

    Since we let \alpha=2t, we now see that \sin\left(2t\right)\cos\left(2t\right)=\tfrac{1}{2  }\sin\left(4t\right)
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