Answer
sin A = 7/25
cos B = 21/29
To find sin(A + B), we use double angle formula.
sin(A + B) = sin A cos B + sin B cos A
sin A = 7/25 , cos B = 21/29
From trigonometric identity, sin²θ + cos²θ = 1
cos A = √(1 - sin²A) = √(1 - (7/25)²)
cos A = √(1 - (49/25))
cos A = √(576/625)
cos A = 24/25
Also, sin B = √(1 - cos²B) = √(1 - (21/29)²)
sin B = √(1 - (441/841))
sin B = √(400/841)
sin B = 20/29
Recall that sin(A + B) = sin A cos B + sin B cos A
sin (A + B) = (7/25 x 21/29) + (20/29 x 24/25)
sin (A + B) = (147/725 + 480/725)
sin (A + B) = (147 + 480)/725
sin (A + B) = 627/725
