Question

Given cos( ) A = 5/7 and cos( ) B = 7/9, using the sum and difference identities, determine the value of sin( ) A + B (You may assume angles A and B exist in the first quadrant).

a) 14/63
b) 10/63
c) -20/63
d) 28/63

Answer 1

The value of sin(A + B) is 10/9.

Step-by-step explanation:

To find the value of sin(A + B), we can use the sum identity for sine: sin(A + B) = sin(A)cos(B) + cos(A)sin(B). Given that cos(A) = 5/7 and cos(B) = 7/9, we can substitute these values into the identity to get: sin(A + B) = sin(A)(7/9) + (5/7)sin(B). Since angles A and B exist in the first quadrant, sin(A) and sin(B) are both positive. Therefore, sin(A + B) = (7/9)(5/7) + (5/7)(7/9) = 35/63 + 35/63 = 70/63 = 10/9.