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Math Help - Trig identities

  1. #1
    dolphinlover527
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    Unhappy Trig identities

    1-{(sin^2)/(1+cos x)}=cos x
    How?
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  2. #2
    Senior Member topher0805's Avatar
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    Is this what you mean?

    Prove that,

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

    If so, then it is not as hard as you think. Everything is already changed to sine and cosine, so half of the work is done.

    First, multiply both sides by 1 + cos x:

    1 + cos x - sin^2 x = cos x + cos^2 x

    Then subtract cos x from both sides:

    <br />
1 - sin^2 x = cos^2 x

    Add sin^2 x to both sides and we now have that:

    cos^2 x + sin^2 x = 1

    This is a trigonometric identity, and therefore you have proved that:

    1 - \frac{sin^2 x}{1 + cos x} = cos x
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  3. #3
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    Hello, dolphinlover527!

    Prove: . 1-\frac{\sin^2\!x}{1+\cos x} \:=\:\cos x

    We have: . 1 - \frac{\sin^2\!x}{1+\cos x} \;\;=\;\;1 - \frac{1-\cos^2\!x}{1+\cos x} \;\;=\;\;1 - \frac{(1-\cos x)(1+\cos x)}{1+\cos x}


    Reduce: . 1 - (1 - \cos x) \;\;=\;\;1 - 1 + \cos x \;\;=\;\;\cos x

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