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 sin C

• 4 cos A cos B cos C

• None of these

Answer 1

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

Explanation:

We have, sin 2A + sin 2B – sin 2C

= (sin 2A + sin 2B) – sin 2C

= `2 sin((2A + 2B)/2) cos((2A - 2B)/2) - sin 2C`

= 2 sin (A + B) cos ( A – B) – sin 2C

= 2 sin C cos (A – B) – 2 sin C cos C

= 2 sin C [cos (A – B) – cos C]

= 2 sin C [cos (A – B) + cos (A + B)]

= 2 sin C (2 cos A cos B)

= 4 cos A cos B sin C