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Math Help - Prove this idenity

  1. #1
    Member smmmc's Avatar
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    Prove this idenity

    Thanks
    Attached Thumbnails Attached Thumbnails Prove this idenity-math.jpg  
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  2. #2
    Super Member Failure's Avatar
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    Quote Originally Posted by smmmc View Post
    Thanks
    Just substitute \tfrac{\sin\theta}{\cos\theta} for \tan\theta and \tfrac{\cos\theta}{\sin\theta} for \cot\theta. After cancelling the denominators on the left side of the equation you get \sin^2\theta+\cos^2\theta=1, which is surely true for all \theta.
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  3. #3
    Member smmmc's Avatar
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    so it becomes

    cos^2theta * sintheta/costheta + sin^2theta * cos theta/sin theta

    = cos theta*sin theta + sin theta*cos theta

    how does this equal to 1 ?

    help please
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  4. #4
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    Hi smmmc

    You forgot that the question is \tan^2\theta and \cot^2\theta, not \tan\theta and \cot\theta
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  5. #5
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    cos^2(x)*tan^2(x)+sin^2(x)*cot^2(x)

    =cos^2(x)\frac{sin^2(x)}{cos^2(x)}+sin^2(x)\frac{c  os^2(x)}{sin^2(x)}

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