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Math Help - Verify Ident.

  1. #1
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    Verify Ident.

    Verify:
    Square root(1+sin(x)/1-sin(x))=1+sin(x)/absolute value(cos(X))
    Hopefully that made some since explained in words:
    The Square Root (of the entire left side of equal sign) 1+sin(x) over 1-sin(x) equals 1 + sin(X) over the absolute value of cos(x)
    Thanks
    AC
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  2. #2
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    Quote Originally Posted by Casas4 View Post
    Okay so i am completely stuck and hopefully you can understand this

    Square root (of the whole thing on left side of = sign) (1+sin(x)/1-sin(x)) = 1+sin(x)/Absolute value cos (x)
    If that didnt make since im sorry
    THanks
    AC
    Left hand side = \sqrt{\frac{1 + \sin x}{1 - \sin x}} = \sqrt{\frac{(1 + \sin x)(1 + \sin x)}{(1 - \sin x)(1 + \sin x)}}


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


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


    = \frac{1 + \sin x}{|\cos x|}


    since 1 + \sin x \geq 0 for all values of x but  -1 \leq \cos x \leq 1.
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