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

Answer 1

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