Question
Fri September 20, 2013 By: Navya Benny

In triangle ABC show that (sin)^2 A/2 = (sin)^ 2 B+C/2 = 1

Expert Reply
Sun September 22, 2013

In a triangle sum of all angles is 180 degrees.

A + B + C = 180o

B + C = 180 - A

B + C/2 = 90 - A/2

sin2 (B + C/2) = sin2 (90 - A/2)

sin2 (B + C/2) = cos2 A/2

 

Hence, 

LHS = sin2 A/2 + sin2 (B + C/2) = sin2 A/2 + cos2 A/2 = 1

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