Math

If A and B are acute angle such that SinA=8/17 and CosB=3/5.Find
1, Cos(A+B)
2, Sin(A+B)
3, Sin(A-B)

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  1. sinA = 8/17 = Y/r.
    X^2 + Y^2 = r^2
    X^2 + 8^2 = (17)^2
    X^2 = (17)^2 - 8^2 = 225
    X = 15.
    cosA = X/r = 15/17.

    cosB = 3/5 = X/r.
    X^2 + Y^2 = r^2.
    3^2 + Y^2 = 5^2
    Y^2 = 5^2 - 3^2 = 16
    Y = 4.
    sinB = Y/r = 4/5.

    1. cos(A+B) = cosA*cosB - sinA*sinB.
    cos(A+B) = 15/17 * 3/5 - 8/17 * 4/5 =
    45/85 - 32/85 = 13/85.

    2. sin(A+B) = sinA*cosB + cosA*sinB.

    The student can solve #2, and #3.

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