If sin A = 3/5 and sin B = 5/13, and angles A and B are acute angles, what is the value of cos(A - B)?
cos A = sqrt (5^2 - 3^2) / 5 = sqrt (16) / 5 = 4/5
cos B = sqrt (13^2 -5^2) /13 = sqrt (144) / 13 = 12 / 13
cos ( A - B) =
cos A cos B + sin A sin B filling in the blanks, we have
(4/5) ( 12/13) + ( 3/5) (5/13) =
(48 + 15) / 65 =
63 / 65
+1671 
