Question

prove that IF A+B+C=180, sin^(A/2)+sin^2(B/2)-sin^2(C/2)=1-2cos(A/2)cos(B/2)sin(C/2)

Answer 1

This would take me sometime, especially as I am sick today, and a bit fuzzy. I'll give it a shot, but I hope you're not in a hurry.

Answer 2

:(

Answer 3

Isn't there square with sin(A/2)?

Answer 4

YES

Answer 5

It might be given that A,B,C constitutes a an equilateral triangkle as analysis is saying thjat it will only be true for A=B=C=60.

Answer 6

It's definitely true. I started with
A+B+C= pi, so A/2 + B/2 + C/2 = 90, and then worked with
a=A/2, b=B/2, c= C/2
start with
cos(a)cos(b)sin(a)
expanded cos(a)cos(b) as 0.5(cos(a-b) + cos(a+b))
It's a bit involved, so I'll type the rest up and post it.

Answer 7

Good luck deciphering this