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Math Help - trigonometric identiy

  1. #1
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    trigonometric identiy

    how would simply/solve (1+cosx)/(sinx) + (sinx)/(1+cosx)?
    please help i've been stuck on thisproblem forever
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  2. #2
    MHF Contributor Amer's Avatar
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    \frac{1+cosx}{sinx}+\frac{sinx}{1+cosx}

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

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

    \frac{1+2cosx}{sinx(1+cosx)}
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  3. #3
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    Quote Originally Posted by Amer View Post
    \frac{1+cosx}{sinx}+\frac{sinx}{1+cosx}

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

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

    \frac{1+2cosx}{sinx(1+cosx)}
    Minor correction: the last step should be

    \frac{{\color{red}2}+2cosx}{sinx(1+cosx)} ,

    which means we can simplify further:

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

    \frac{2}{sinx}

    2csc\ x


    01
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  4. #4
    MHF Contributor Amer's Avatar
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    Thanks very much I forget it
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  5. #5
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    thank you guys so much
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