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Math Help - Simultaneous trigonometric equations?

  1. #1
    Super Member fardeen_gen's Avatar
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    Simultaneous trigonometric equations?

    If tan(A - B) = 1 & sec (A + B) = 2/√3, find the smallest positive values of A & B and also their most general values.

    I have no idea how to attempt this problem. Can anybody help?
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  2. #2
    MHF Contributor kalagota's Avatar
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    A-B = \tan^{-1} 1 = \frac{\pi}{4}

    \sec (A+B) = \frac{1}{\cos (A+B)} = \frac{2}{\sqrt{3}} \Rightarrow \cos (A+B) = \frac{\sqrt{3}}{2}

    A+B = \cos^{-1}\left(\frac{\sqrt{3}}{2}\right) = \frac{\pi}{6}
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  3. #3
    Super Member fardeen_gen's Avatar
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    Kalagota, thanks for the method. However if we proceed, we get value of A= 37.5 degrees and B = - 7.5 degrees. Answer asked is smallest positive value. How do we find that?(answers: A = 187.5 B = 142.5)
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