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In ∆ABC , sin^2(A/2)+sin^2(B/2)+sin^2(C/2) = |
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Answer» Answer: Step-by-step EXPLANATION: (a−B) 2 cos 2
2 C +(a+b) 2 2
2 C
=a 2 +b 2 +2ab(sin 2
2 C −cos 2
2 C ) =a 2 +b 2 +2ab(2SIN 2
2 C −1) But sin 2 C = (s−a)(s−b)
where s= 2 a+b+c
∴ a 2 +b 2 +2ab(2sin 2
2 C −1) =a 2 +b 2 +2ab( 2ab (c+b−a)(c+a−b) −1) =a 2 +b 2 +c 2 −(b−a) 2 −2ab =c 2 |
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