Question

cos (b-c/2)=(b+c/a) sin A/2​

Answer 1

Step-by-step explanation:

Using sine law, we have: (b+c/2) sin A/2 = (k sin B + k sin C/ k sinA) x sin A/2 = (sin B + sin C/ sinA) x sin A/2 = [2 sin (B+C)/2. cos (B-C)/2. sin A/2] / 2 sin A/2. cosA/2 = [sin (B+C)/2. cos (B-C)/2.] / cosA/2 = [sin [90 - A/2]. cos (B-C)/2.] / cosA/2 = [cos A/2]. cos (B-C)/2.] / cosA/2 = cos (B-C)/2 Hence, a cos (B-C/2)=(b+c) Sin A/2