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Question
If A + B + C = 180°, prove that sin(B + C − A) + sin(C + A − B) + sin(A + B − C) = 4 sin A sin B sin C
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Solution
Now A + B + C = 180°
So B + C = 180° – A
sin(B + C – A) = sin(180° – A – A)
= sin(180° – 2A) = sin 2A
Now L.H.S = sin 2A + sin 2B + sin 2C
= 4 sin A sin B sin C ......[From (i)]
= R.H.S
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