If A + B + C = π, prove that sin A + sin B + sin C = 4cos A/2 cos B/2 cos C/2

Question

If A + B + C = π, prove that

sin A + sin B + sin C = 4cos \(\frac{A}2\) cos\(\frac{B}2\)cos\(\frac{C}2\)

Answer 1

sin A + sin B + sin C 

Using,

Since A + B + C = π 

→ B + C = 180 - A

And,

Using, sin2A = 2sinAcosA

→ B + C = 180 - A

And,