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Math Help - Help with a trig proof...

  1. #1
    Junior Member
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    Question Help with a trig proof...

    I would appreciate some help proving the following:

    (sin of theta/1-cos theta) - (1+cos theta/ sin theta)= 0
    Thanks for looking, and thanks in advance.
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  2. #2
    Member great_math's Avatar
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    (sin of theta/1-cos theta) - (1+cos theta/ sin theta)= 0

    =\frac{\sin\theta}{1-\cos\theta}-\frac{1+\cos\theta}{\sin\theta}

    =\frac{\sin^2\theta-(1-\cos\theta)(1+\cos\theta)}{(1-\cos\theta)(\sin\theta)}

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

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

    =0=R.H.S
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  3. #3
    Member SENTINEL4's Avatar
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    You have

    \frac{sin\vartheta}{1-cos\vartheta}-\frac{1+cos\vartheta}{sin\vartheta}

    You multiply the first fraction with sin\vartheta and the second with 1-cos\vartheta so you get...

    \frac{sin^2\vartheta}{(1-cos\vartheta)sin\vartheta}-\frac{(1+cos\vartheta)(1-cos\vartheta)}{(1-cos\vartheta)sin\vartheta} = \frac{sin^2\vartheta}{(1-cos\vartheta)sin\vartheta}-\frac{1-cos\vartheta+cos\vartheta-cos^2\vartheta}{(1-cos\vartheta)sin\vartheta} = \frac{sin^2\vartheta+cos^2\vartheta-1}{(1-cos\vartheta)sin\vartheta}

    But we know that sin^2\vartheta+cos^2\vartheta=1 so

    \frac{1-1}{(1-cos\vartheta)sin\vartheta} = \frac{0}{(1-cos\vartheta)sin\vartheta} = 0
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  4. #4
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    thanks!

    thank you both for the quick and useful help!
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