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Math Help - another simple question

  1. #1
    Junior Member lanzailan's Avatar
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    Mar 2009
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    another simple question

    Hi people..
    ok, this question is actually very simple and i did it 5 times but i didn't get the answer as provided.

    here is the question..
    A is in 3rd quadrant with cos A=-24/25 and B in the 2nd quadrant with cos B=-8/17. Find tan(A+B).

    Answer:-304/297<<----- i believe that the answer provided is wrong!

    can anybody prove that i'm wrong?
    thanks in advance
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  2. #2
    MHF Contributor
    Grandad's Avatar
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    South Coast of England
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    Trigonometry

    Hello lanzailan
    Quote Originally Posted by lanzailan View Post
    Hi people..
    ok, this question is actually very simple and i did it 5 times but i didn't get the answer as provided.

    here is the question..
    A is in 3rd quadrant with cos A=-24/25 and B in the 2nd quadrant with cos B=-8/17. Find tan(A+B).

    Answer:-304/297<<----- i believe that the answer provided is wrong!

    can anybody prove that i'm wrong?
    thanks in advance
    \tan A = \frac{7}{24}, \tan B = -\frac{15}{8}

    \Rightarrow \tan (A+B) = \frac{\tan A + \tan B}{1 - \tan A \tan B}

    = \left(\frac{7}{24} - \frac{15}{8}\right) \div \left(1 + \frac{7}{24}\times\frac{15}{8}\right)

    = \frac{7\times 8 - 15 \times 24}{24 \times 8 + 7\times 15}

    =-\frac{304}{297}

    Grandad
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  3. #3
    Junior Member lanzailan's Avatar
    Joined
    Mar 2009
    Posts
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    ok now i see where i did it wrong..
    in 3rd quadrant tanA should be positive.

    thanks Grandad
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