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Math Help - Trigonometric identity help

  1. #1
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    Trigonometric identity help

    Hi all,

    I am stuck on proving these two problems:

    (csc theta - sin theta)^2 = cot^2theta - cos^2theta

    and

    (1+cos2theta/cos^2theta)=2

    I know I need to use double angle identities in the second one, but I have been stuck on how to get going.
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  2. #2
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    Quote Originally Posted by Bikkstah View Post
    Hi all,

    I am stuck on proving these two problems:

    (csc theta - sin theta)^2 = cot^2theta - cos^2theta

    and

    (1+cos2theta/cos^2theta)=2

    I know I need to use double angle identities in the second one, but I have been stuck on how to get going.
    (\csc{\theta} - \sin{\theta})^2 = \csc^2{\theta} - 2\csc{\theta}\sin{\theta} + \sin^2{\theta}

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

     = \csc^2{\theta} - 1 - (1 - \sin^2{\theta})

     = \cot^2{\theta} - \cos^2{\theta}.
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  3. #3
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    Can anyone help with (1 + Cos2theta/cos^2theta)=2? I know it's true by setting theta equal to a real angle like 30 degrees, but I don't know how to prove it using just identities.
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  4. #4
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    Quote Originally Posted by Bikkstah View Post
    (1+cos2theta/cos^2theta)=2
    Use the identity \cos (2\theta) = 2\cos^2 \theta -1

    Spoiler:
    \frac{1+\cos (2\theta)}{\cos^2 \theta}

    \frac{1+2\cos^2 \theta -1}{\cos^2 \theta}

    This cancels down to 2
    Last edited by e^(i*pi); April 2nd 2010 at 02:19 AM. Reason: sign error in solution
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  5. #5
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    Thank you both so much!
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