Question

If A + B + C = π, then sin 2A + sin 2B + sin 2C is equal to ______.

Options

• 4 sin A sin B sin C

• 4 cos A cos B cos C

• 2 cos A cos B cos C

• 2 sin A sin B sin C

Answer 1

If A + B + C = π, then sin 2A + sin 2B + sin 2C is equal to 4 sin A sin B sin C.

Explanation:

B + C = π – A

`\implies` sin (B + C) = sin (π – A) = sin A

∴ sin 2A + sin 2B + sin 2C

= 2 sin A cos A + 2 sin (B + C) cos (B – C)

= 2 sin A [cos A + cos (B – C)]

= 2 sin A [cos (B – C) – cos (B + C)]

= 2 sin A [2 sin B sin C]

= 4 sin A sin B sin C