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Math Help - [SOLVED] Pre-Cal/Trig Proofs

  1. #1
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    [SOLVED] Pre-Cal/Trig Proofs

    Can someone please help me prove that sin^2(x) - cos^2(x) = 1-2cos^2(x)
    I don't even know where to start.
    Also, I need help on this problem: tan(x) + sec(x) = cos(x)/(1-sinx)
    I've started on the second one, but got stuck. I would greatly appreciate any help.
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  2. #2
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    for the first problem, if you simply turn your sin^2(x) into 1-cos^2(x) and combine like terms they should be equal right off the bat. It took me forever to come up with that though, and i can't think of what to do for the second one but just try converting everything into sin's and cos's to start. I find it helps when i can't think of what to do. Hope i could help
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  3. #3
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    Thanks! Now that I know how to do it, it seems simple

    I did turn everything in the second problem to sin's and cos's, but came up with almost the opposite answer that I'm supposed to have. (sinx+1)/cosx.
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  4. #4
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    Quote Originally Posted by Purpledog100 View Post
    Thanks! Now that I know how to do it, it seems simple

    I did turn everything in the second problem to sin's and cos's, but came up with almost the opposite answer that I'm supposed to have. (sinx+1)/cosx.
    now rationalize by multiplying Numerator and Denominator by (1 - sin x)

     <br />
\frac {1+\sin x}{\cos x}<br />

     <br />
=\frac {1+\sin x}{\cos x}\times \frac {1-\sin x}{1-\sin x}<br />

     <br />
=\frac {1-\sin^2 x}{\cos x(1-\sin x)}<br />

    Now change 1-\sin^2 x into \cos^2 x in the numerator

    can you finish ???
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  5. #5
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    Yep, I got it. Thanks a lot!
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