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Math Help - Verify that √((1-cosx)/(1+cosx)) = (1-cosx)/|sinx|

  1. #1
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    Verify that √((1-cosx)/(1+cosx)) = (1-cosx)/|sinx|

    For this problem we're supposed to prove/verify that:

    √((1-cosx)/(1+cosx)) = (1-cosx)/|sinx|

    Also, if someone could explain why the sinx in the right side has to be absolute value, that would be appreciated. Thank you
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  2. #2
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    \sqrt{\frac{1-\cos{x}}{1+\cos{x}}} \cdot \sqrt{\frac{1-\cos{x}}{1-\cos{x}}} =

    \frac{1 - \cos{x}}{\sqrt{1 - \cos^2{x}}} =

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

    \frac{1 - \cos{x}}{|\sin{x}|}


    basic algebra ... \sqrt{a^2} = |a|
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  3. #3
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    Thank you, I understand the proof now!

    A little clarification in this matter:
    |a| = √a^2

    is this because its a^2 and not (-a)^2? (So if it were (-a)^2 it'd be -|a| ?)

    Thanks!
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  4. #4
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    Quote Originally Posted by SMA777 View Post
    Thank you, I understand the proof now!

    A little clarification in this matter:
    |a| = √a^2

    is this because its a^2 and not (-a)^2? (So if it were (-a)^2 it'd be -|a| ?)

    Thanks!
    There are always two square roots to any number.

    i.e. \sqrt{a^2} = a or \sqrt{a^2} = -a

    Notice that both answers have a "size" of a.

    This "size" is denoted with an absolute value.

    So \sqrt{a^2} = |a| is correct, because it's saying the answer is something of "size" a.
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