Question

If sin A = 3/5, cos B = 4/5 find sin(A + B) and cos(A – B). Where A and B are acute angles.

Answer 1

Given sin A = 3/5, cos B = 4/5

⇒ cos A = 4/5 & sin B = 3/5

∵ sin2A + cos2A = 1

(i) sin(A + B) = sinA cosB + cosA sinB

= 3/5. 4/5 + 4/5.3/5 = 24/25

(ii) cos(A – B) = COSA COSB + sinA sinB

= 4/5.4/5 + 3/5.3/5 = 16/25 + 9/25 = 25/25 = 1