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Math Help - Prove this trigonometric identity

  1. #1
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    Prove this trigonometric identity

    Can somebody show me the steps to prove this question.

    Prove that:

    cos x + cos x = 2sec x
    1 - sin x 1 + sin x
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  2. #2
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    {cosx}/{1-sinx} + {cosx}/{1+sinx} = {(cosx)(1+sinx)+(cosx)(1-sinx)}/{(1-sinx)(1+sinx)}=

    ={(cosx)(1+sinx)+(cosx)(1-sinx)}/{(1-(sinx)^2}=

    ={(cosx)(1+sinx)+(cosx)(1-sinx)}/{(cosx)^2}=

    ={(1+sinx)+(1-sinx)}/{(cosx)}=

    ={2}/{cosx}=

    =2secx
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  3. #3
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    Quote Originally Posted by GAVREED2 View Post
    Can somebody show me the steps to prove this question.

    Prove that:

    cos x + cos x = 2sec x
    1 - sin x 1 + sin x
    working on the left side, get a common denominator ...

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

    ... then add the two fractions.
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