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Math Help - Calculate!

  1. #1
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    Calculate!

    Given that \frac{cos(A-B)}{cos(A+B)}=\frac{7}{5}, prove that cosAcosB = 6sinAsinB and deduce a relationship between tanA and tanB. Given further that A+B=45^\circ, calculate the value of tanA+tanB.

    I have already proved the equation.

    I have also tried to deduce the relationship between tanA and tanB,

     cosAcosB=6sinAsinB

    \frac{cosAcosB}{sinAsinB}=\frac{1}{6}

    [Math]tanAtanB=\frac{1}{6}[/tex]

    But am not sure if I am on the right track. Lastly, need help with calculating the value of tanA+tanB
    Last edited by Punch; January 22nd 2010 at 01:40 AM.
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  2. #2
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    Yes, you are on the right track (except that the 6 should be 1/6 — remember that tan = sin/cos, not cos/sin). For the last part, use the formula \tan(A+B) = \frac{\tan A + \tan B}{1-\tan A\tan B}.
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