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Math Help - Trigonometry Identity Rearrangement

  1. #1
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    Trigonometry Identity Rearrangement

    Can someone show me how \sin ^22\theta equal to 1-\cos 4\theta?

    Thanks in advance.
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  2. #2
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    Hello,

    Quote Originally Posted by Air View Post
    Can someone show me how \sin ^22\theta equal to 1-\cos 4\theta?

    Thanks in advance.
    \cos 4 \theta=\cos (2 \cdot 2 \theta)

    Using the identity \cos 2a=1-2 \sin^2a, we get :

    \cos 4 \theta=1-2 \sin^2 2\theta

    \sin^2 2 \theta=\frac{1-\cos 4 \theta}{\color{red}2}

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    ...So if we had something like:

    \sin^2 6\theta, would that be \frac{1 - \cos 12 \theta}{2}?
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  4. #4
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    Quote Originally Posted by Air View Post
    ...So if we had something like:

    \sin^2 6\theta, would that be \frac{1 - \cos 12 \theta}{2}?
    Yes =)

    Always refer to double angle properties ^^
    It's just a matter of substitution.
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