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Math Help - establish this identity

  1. #1
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    establish this identity

    (1+ cos^2 theta)(1- cot^2 theta)= 1


    I have no idea how (1+ cos^2 theta)(1- cot^2 theta) could possibly equal to 1. Any ideas?
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  2. #2
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    Re: establish this identity

    Quote Originally Posted by avatartiger2 View Post
    (1+ cos^2 theta)(1- cot^2 theta)= 1


    I have no idea how (1+ cos^2 theta)(1- cot^2 theta) could possibly equal to 1. Any ideas?
    you sure it's not (1 - \cos^2{\theta})(1 + \cot^2{\theta}) = 1 ?
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  3. #3
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    Re: establish this identity

    Idea: First, unpack cotangent in terms of sine and cosine. Then simplify (multiply out - or something even better if you see it) the left hand side.
    Also, I believe that skeeter's correct about the actual problem intended.
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  4. #4
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    Re: establish this identity

    yeah! i looked over the problem and I think the textbook might have switched the signs! (1-cos^2 theta)(1+ cot^2 theta) does simplify to 1. I kept doing the other problem over and over again. thanks for telling me! what a relief!
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