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Math Help - Verification problems

  1. #1
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    Verification problems

    1. sinx+cosx/tan^2x-1 = cos^2x/sinx-cosx

    I've tried everything(converting to sines and cosines, factoring, etc.) and even my teacher couldn't figure it out...

    2. 1+tanx/1-tanx = sec^2x+2tanx/2-sec^2x


    I make everything more and more complicated when I try and verify this one from the right side
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  2. #2
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    Quote Originally Posted by clay10 View Post
    1. sinx+cosx/tan^2x-1 = cos^2x/sinx-cosx

    I've tried everything(converting to sines and cosines, factoring, etc.) and even my teacher couldn't figure it out...

    2. 1+tanx/1-tanx = sec^2x+2tanx/2-sec^2x


    I make everything more and more complicated when I try and verify this one from the right side
    \frac{\sin{x} + \cos{x}}{\tan^2{x} - 1}

    multiply numerator and denominator by \cos^2{x} ...

    \frac{\cos^2{x}\sin{x} + \cos^3{x}}{\sin^2{x} - \cos^2{x}}

    factor ...

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

    \frac{\cos^2{x}}{\sin{x} - \cos{x}}


    for the second one, change sec^2{x} to \tan^2{x} + 1 on the RHS, then factor both numerator and denominator.
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  3. #3
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    thanks a lot. I was confused why you chose cos^2x but I realized we have never used any identities from the other side of the equation to the more complicated side.
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