Question

If p,q,rare the interior angles of Δpqr show that sin(p+q/2)=cos(r/2)

Answer 1

In a ΔPQR, the sum of angles is = 180 deg or π.

P+Q+R = π 

P+Q = π - R

(P+Q)/2 = π/2 - R/2

Sin [ (P+Q)/2 ] = Sin [ π/2 - R/2 ] = Cos (R/2)