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Math Help - Trigonometric Identity Problem

  1. #1
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    Trigonometric Identity Problem

    This is probably pretty simple, I cant figure it out though.

    "Prove the identity (T = Theta): (cos(2T)) / (1 + sin(2T)) = (cot(T) - 1) / (cot(T) + 1)"


    So...
    ((cos(T)^2) - (sin(T)^2)) / (1 + 2*sin(T)*cos(T)) = (cos(T) - sin(T)) / (cos(T) + sin(T))

    (cos(T) + sin(T)) * ((cos(T)^2) - (sin(T)^2)) = (cos(T) - sin(T)) * (1 + 2*sin(T)*cos(T))

    (cos(T) + sin(T)) * (cos(T) - sin(T)) = (1 + 2*sin(T)*cos(T))

    ((cos(T)^2) - (sin(T)^2)) = (1 + 2*sin(T)*cos(T))

    At this point I am stuck. What do I need to do now?
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  2. #2
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  3. #3
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    \frac{\cos(2t)}{1 + \sin(2t)} = \frac{\cot{t} - 1}{\cot{t} + 1}

    multiply the right side by \frac{\sin{t}}{\sin{t}} ...

    \frac{\cos(2t)}{1 + \sin(2t)} = \frac{\cos{t} - \sin{t}}{\cos{t} + \sin{t}}

    multiply right side by \frac{\cos{t} + \sin{t}}{\cos{t} + \sin{t}} ...

    \frac{\cos(2t)}{1 + \sin(2t)} = \frac{\cos^2{t} - \sin^2{t}}{\cos^2{t} + 2\sin{t}\cos{t} + \sin^2{t}}

    \frac{\cos(2t)}{1 + \sin(2t)} = \frac{\cos(2t)}{1 + \sin(2t)}
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