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Math Help - Proving Trig Identity again

  1. #1
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    Proving Trig Identity again

    Prove:

    <br />
(cot(x) + cosec(x))^2 = \frac{1+cos(x)}{1-cos(x)}<br />

    And i can get this far but no further:

    <br />
\frac{cos^{2}(x) + 2cos(x) + 1}{1 - cos^{2}(x)}<br />

    Anyone see my fault? Mybe i need to factorise the top of the factor...hmmmm
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Quote Originally Posted by aceband View Post
    Prove:

    <br />
(cot(x) + cosec(x))^2 = \frac{1+cos(x)}{1-cos(x)}<br />

    And i can get this far but no further:

    <br />
\frac{cos^{2}(x) + 2cos(x) + 1}{1 - cos^{2}(x)}<br />

    Anyone see my fault? Mybe i need to factorise the top of the factor...hmmmm
    (cotx+cosecx)^2=(\frac{cosx}{sinx}+\frac{1}{sinx})  ^2

    = (\frac{cosx+1}{sinx})^2

    = \frac{(cosx+1)^2}{sin^2x}

    = \frac{(1+cosx)^2}{1-cosx^2}

    = \frac{(1+cosx)^2}{(1+cosx)(1-cosx)}

    = \frac{1+cosx}{1-cosx}
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  3. #3
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    Really sorry but can't see how to get that to the final stage :S
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  4. #4
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    Ignore that comment i see it thanks
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