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Math Help - Trigonometric identities.

  1. #1
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    Trigonometric identities.

    (sinθ-cosθ)^2
    = sin^2 θ-2sinθcosθ-cos^2 θ

    is this all?? what else can i do?
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  2. #2
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    Not sure what you are trying to do but

     (\sin\theta-\cos\theta)^2 = (\sin\theta-\cos\theta)(\sin\theta-\cos\theta)= \sin^2\theta-2\sin\theta\cos\theta+\cos^2\theta \neq \sin^2\theta-2\sin\theta\cos\theta-\cos^2\theta<br />

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

    and 2\sin\theta\cos\theta = \sin 2\theta

    Good luck!
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  3. #3
    MHF Contributor
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    Quote Originally Posted by somanyquestions View Post
    (sinθ-cosθ)^2
    = sin^2 θ-2sinθcosθ+cos^2 θ

    is this all?? what else can i do?
    two identities involved here ...

    (1) the basic Pythagorean identity ...

    \sin^2{x} + \cos^2{x} = 1

    (2) the double angle identity for sine ...

    \sin(2x) = 2\sin{x}\cos{x}

    ...

    \sin^2{\theta} - 2\sin{\theta}\cos{\theta} + \cos^2{\theta}  =

    1 - 2\sin{\theta}\cos{\theta} =

    1 - \sin(2\theta)
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