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Math Help - more problem with identities, what am i doing wrong?

  1. #1
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    more problem with identities, what am i doing wrong?

    Sin ^ 2 ( 1 + cot ^ 2) - 1 = 0

    so I tried to solve like this
    (1-cot^2)(1+cot^2) -1
    1+cot^ 4 - 1
    cot^ 4
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  2. #2
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    Quote Originally Posted by melvis View Post
    Sin ^ 2 ( 1 + cot ^ 2) - 1 = 0

    so I tried to solve like this
    (1-cot^2)(1+cot^2) -1
    1+cot^ 4 - 1
    cot^ 4
    What you have said at the moment is meaningless.

    I assume you mean that you are trying to prove

    \sin^2{x}(1 + \cot^2{x}) - 1 = 0.


    \sin^2{x}\left(1 + \cot^2{x}\right) - 1 = \sin^2{x}\left(1 + \frac{\cos^2{x}}{\sin^2{x}}\right) - 1

    =\sin^2{x}\left(\frac{\sin^2{x} + \cos^2{x}}{\sin^2{x}}\right) - 1

    =\sin^2{x}\left(\frac{1}{\sin^2{x}}\right) - 1

     = 1 - 1

     = 0.
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