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if sinA+sinB=x and cosA-cosB=y then find tan[(A-B)/2]

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Aditya

  1. use your sum-to-product formulas.
    sinA + sinB = 2 sin (A+B)/2 cos (A-B)/2
    now use the formula for sum of cosines, and recall that
    tanθ = sinθ / cosθ

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    oobleck

  2. Two of the lesser known identities are:
    sinA + sinB = 2sin[(A+B)/2]cos[(A-B)/2] and
    cosA - cosB = -2sin[A+B)/2]sin[A-B)/2]
    so
    x/y = ( 2sin[(A+B)/2]cos[(A-B)/2] ) / (-2sin[A+B)/2]sin[A-B)/2] )
    x/y = - cos[(A-B)/2] / sin[A-B)/2]
    x/y = - cot[(A-B)/2]
    tan[(A-B)/2] = -y/x

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    Reiny

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