Question

For positive acute angles A and B, it is known that sin A= 7/25 and cos B= 21/29. Find the value of sin(A + B) in simplest form.

Answer 1

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