Posted by **Ada Enugu** on Tuesday, January 29, 2013 at 1:07am.

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)

- Math -
**Henry**, Thursday, January 31, 2013 at 3:36pm
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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