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Math Help - unsure

  1. #1
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    Talking unsure

    I kind of think I know what I could do, but I am unsure how to proceed.

    Q: Find a + b in radians if tan a = M and tan b = N and (3M+3)(2N+2)= 12.
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  2. #2
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    Quote Originally Posted by mathAna1ys!5
    I kind of think I know what I could do, but I am unsure how to proceed.

    Q: Find a + b in radians if tan a = M and tan b = N and (3M+3)(2N+2)= 12.
    If \tan a=M and \tan b=N then,
    \tan (a+b)=\frac{\tan a+\tan b}{1-\tan a\tan b}=\frac{M+N}{1-MN} (1)

    Now since (3M+3)(2N+2)=12 factor and divide thus, (M+1)(N+1)=2 now open parantheses (remember to FOIL) thus,
    MN+N+M+1=2 thus,
    N+M=1-MN substitute that into (1):
    thus,
    \tan (a+b)=\frac{1-MN}{1-MN}=1
    thus,
    a+b=\frac{\pi}{4} as one anwer.
    Q.E.D.

    (Note it was assumed that a,b was non-coterminal was \frac{\pi}{2} or \frac{3\pi}{2}).
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