Question

Prove that sin (A+B)/2 = cos C/2

Answer 1

we know that A+B+C = 180
⇒ A+B = 180-C
⇒(A+B)/2 = (180-C)/2
⇒(A+B)/2 = 90 - C/2

So sin (A+B)/2
= sin (90 - C/2)
= cos (C/2)                   (since sin(90-β) = cosβ)