Question

A+B+C = π then prove that A=B=C​

Answer 1

a+b+c=π

a+b=π-c

∴ a/2 + b/2 = π/2 - c/2

sin(a/2+b/2) = sin(π/2-c/2) = cos c/2

cos(a/2+b/2) = cos(π/2-c/2) = sin c/2

L:H:S = sin a + sin b + sin c

= 2sin(a/2+b/2).cos(a/2-b/2) + 2sin c/2.cos c/2

= 2cos c/2.cos(a/2-b/2) + 2sin c/2.cos c/2

= 2cos c/2 [cos(a/2-b/2) + sin c/2]

= 2cos c/2 [cos(a/2-b/2) + cos(a/2+b/2)

= 2cos c/2 * 2cosa/2.cosb/2

= 4cos a/2.cos b/2.cos c/2

= R:H:S