Published by:
CGP EDU Academic Team
Published on: August 11, 2026
If A + B + C = 0º then prove that sin 2A + sin 2B + sin 2C= – 4 sin A sin B sin C
Text Solution
Verified by ExpertsThe correct answer is:
A
A + B + C = 0º ⇒ B +C = –A
sin2A + 2 sin (B + C) cos (B – C)
= 2 sin A cos A + 2 sin (B + C) cos (B – C)
= 2 sin A cos A – 2 sin A cos (B – C)
= – 2 sin A [cos (B – C) – cos A]
= – 2 sin A [cos (B – C) – cos (B + C)]
= – 2 sin A [2 sin sin ]
= – 4 sin A sin B sin C
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