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Math Help - simplifying expressions

  1. #1
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    simplifying expressions

    Simplify:

    1. sinx cos2x / cosx sin2x

    sinx cos2x - sin2x / 2 sinx cosx

    sinx ( cos2x - 1) / 2 sinx cosx


    solution: 1 - 1/2 cos2x

    I am not sure if what I did is right and I don't know what to do next. May you help me?? Thanks for the answers.
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  2. #2
    Forum Admin topsquark's Avatar
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    Re: simplifying expressions

    Quote Originally Posted by Atalante View Post
    Simplify:

    1. sinx cos2x / cosx sin2x

    sinx cos2x - sin2x / 2 sinx cosx

    sinx ( cos2x - 1) / 2 sinx cosx


    solution: 1 - 1/2 cos2x

    I am not sure if what I did is right and I don't know what to do next. May you help me?? Thanks for the answers.
    Parenthesis would be of some benefit here.

    The numerator...You forgot a multiple of sin(x):
    sin(x) ~ cos(2x) = sin(x) \[cos^2(x) - sin^2(x) \]

    The denominator you also forgot a cos(x):
    cos(x)~sin(2x) = cos(x) \[ 2~sin(x)~cos(x) \]

    -Dan
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  3. #3
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    Re: simplifying expressions

    Quote Originally Posted by Atalante View Post
    Simplify:

    1. sinx cos2x / cosx sin2x

    sinx cos2x - sin2x / 2 sinx cosx

    sinx ( cos2x - 1) / 2 sinx cosx


    solution: 1 - 1/2 cos2x

    I am not sure if what I did is right and I don't know what to do next. May you help me?? Thanks for the answers.
    \displaystyle \begin{align*} \frac{\sin{(x)}\cos{(2x)}}{\cos{(x)}\sin{(2x)}} &= \frac{\sin{(x)}\left[ \cos^2{(x)} - \sin^2{(x)} \right]}{ \cos{(x)} \left[ 2\sin{(x)}\cos{(x)} \right] } \\ &= \frac{\cos^2{(x)} - \sin^2{(x)}}{2\cos^2{(x)}} \\ &= \frac{\cos^2{(x)} - \left[ 1 - \cos^2{(x)} \right]}{2\cos^2{(x)}} \\ &= \frac{2\cos^2{(x)} - 1}{2\cos^2{(x)}} \\ &= 1 - \frac{1}{2\cos^2{(x)}} \end{align*}
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