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Math Help - need help with trig proof thing!!!!!!!!!!!!

  1. #1
    dood
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    Talking need help with trig proof thing!!!!!!!!!!!!

    how do u prove : sec(A-B) = cos(A+B) / ( cosA^2 - sinB^2 )
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  2. #2
    Eater of Worlds
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    Use the subtraction and addition formulas.

    rewrite the left side as:

    \frac{1}{cosAcosB+sinAsinB}

    Multiply top and bottom by cosAcosB-sinAsinB

    and you should be able to hammer it into the right side.

    \frac{1}{cosAcosB+sinAsinB}\cdot\frac{cosAcosB-sinAsinB}{cosAcosB-sinAsinB}

    \frac{cosAcosB-sinAsinB}{cos^{2}Acos^{2}B-sin^{2}A\cdot{sin^{2}}B}

    \frac{\overbrace{cosAcosB-sinAsinB}^{\text{cos(A+B)}}}{cos^{2}A-sin^{2}B}

    \frac{cos(A+B)}{cos^{2}A-sin^{2}B}
    Last edited by galactus; July 5th 2007 at 02:38 PM.
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  3. #3
    Bar0n janvdl's Avatar
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    Quote Originally Posted by dood View Post
    how do u prove : sec(A-B) = cos(A+B) / ( cosA^2 - sinB^2 )
    Haven't checked this, but logic tells me that:

     \frac{ cos(A+B) }{( cos A^2 - Sin B^2 )} = \frac{ cos (A+B) }{ (cos (A-B)) \ (cos (A + B)) } = \frac{1}{ cos (A-B)} = sec (A - B)
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