Posted by Ada Enugu on .
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(AB)

Math 
Henry,
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.