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Math Help - Proving trigonometric identities

  1. #1
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    Proving trigonometric identities

    I had a worksheet with quite a few on it and there are two that I just cannot figure out.
    The first one is:
    (1-cos x)^2 + 2 cos x = sin^2 x + 2 cos^2 x
    I know that sin^2 x = 1-cos^2 x
    so I replaced it so that it is
    1-cos^2 x + 2 cos^2 x

    I'm not sure if that is even in the right direction but I would really appreciate some help.

    The second one is:
    \frac {1+\cos x}{1-\cos x} = \frac {(1+\cos x)^2}{\cos^2 x}

    I tried multiplying the left side by the denominater's conjugate and just got
    \frac {(1+\cos x)^2}{1-\cos^2 x}
    from there I don't know where to go or if I'm even on the right track. Thanks for any help!
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  2. #2
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    Quote Originally Posted by LoveBeachForever View Post
    I had a worksheet with quite a few on it and there are two that I just cannot figure out.
    The first one is:
    (1-cos x)^2 + 2 cos x = sin^2 x + 2 cos^2 x
    I know that sin^2 x = 1-cos^2 x
    so I replaced it so that it is
    1-cos^2 x + 2 cos^2 x

    I'm not sure if that is even in the right direction but I would really appreciate some help.
    (1-cos x)^2 + 2 cos x = sin^2 x + 2 cos^2 x

    Distribute (foil) the left side:

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

    Combine like terms:

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

    Use trig identity sin^2 x + cos^2 x = 1 on left:

    sin^2 x + cos^2 x + cos^2 x = sin^2 x + 2 cos^2 x

    Combine like terms:

    sin^2 x + 2 cos^2 x = sin^2 x + 2 cos^2 x




    Your second one is started well. Use a popular trig identity to help with the left side denominator then notice there are just so many things that are being squared everywhere ...
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  3. #3
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    okay...

    Thanks so much for the first one!!

    Quote Originally Posted by wytiaz View Post
    Use a popular trig identity to help with the left side denominator then notice there are just so many things that are being squared everywhere ...
    Do you mean change <br />
\frac {(1+\cos x)^2}{1-\cos^2 x} to <br />
\frac {(1+\cos x)^2}{\sin^2 x}?

    After that it still doesn't really make sense to me...
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  4. #4
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    I do mean that. And then, look at the bottom of the left side. Try and replace that with something, using what should be the most familiar trig identity you've seen so far (that my class is learning tomorrow actually).

    Then hey, everything is squared... how about we root everything.
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  5. #5
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    That doesn't really make much sense to me....Honestly, the only thing I know to change sin^2 x with is 1-cos^2 x which would just put me back to where I was....And to me, that is the most familiar trig identity...
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