Trigonometry.

Use the given information to evaluate cos (a-b).
Cot a = 3/4, cot b = 24/25; pi<a<3pi/2, 3pi/2<b<2pi.

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  1. since a is in QIII,
    sina = -4/5
    cosa = -3/5

    You sure that's not cos b = 24/25? cot < 0 in QIV. If so, then we have a 7-24-25 triangle.

    sinb = 7/25
    cosb = 24/25

    now just use your difference formula:

    cos(a-b) = cosa cosb + sina sinb

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    posted by Steve

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