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Math Help - Urgent Proving Identities

  1. #1
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    Urgent Proving Identities

    Prove that
    tan A - (sec A sin^3A / 1 + cos A ) = sin A

    Obtained from my Workings

    (sin A / cos A) - (sin^3A / cos A + cos^2 A )
    (From here on I don't know what to do aside from subtracting it)


    Prove that

    sin^3 A / cos A - cos^3A = tan A

    Obtained from my Workings: Can't think of Any

    Thanks, hoping for a fast reply

    Arnold,
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  2. #2
    Super Member
    Joined
    Jun 2008
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    1. \tan{A} - \frac{\sec{A}\sin^3{A}}{1+\cos{A}}

    This can be rewritten as:
    \tan{A} \left( 1 - \frac{\sin^2{A}}{1+\cos{A}}\right)

    Recall that \sin^2{\theta} = 1-\cos^2{\theta} = (1-\cos{\theta})(1+\cos{\theta})<br />
    2. \frac{\sin^3{A}}{\cos{A}-\cos^3{A}}

    Pull one factor of each sine and cosine out:
    \frac{\sin{A}}{\cos{A}} \cdot \frac{\sin^2{A}}{1-\cos^2{A}}

    Can you do it now?
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