Question

In \( \Delta ABC \), if \( \sin 2A + \sin 2B + \sin 2C = \frac{\cos A + \cos B + \cos C - 1}{\cos A + \cos B + \cos C - 1} \), then:

• A. \( 2[\sin A + \sin B + \sin C] \)
• B. \( \sin A + \sin B + \sin C \)
• C. \( 4[\sin A + \sin B + \sin C] \)
• D. \( 8[\sin A + \sin B + \sin C] \)

Hint:

For solving trigonometric identities in triangles, use known identities and symmetry of the angles.

Answer 1

The Correct Option is A

We are given a trigonometric expression involving the angles of a triangle. By simplifying the expression and using the known identities, we find that the result simplifies to \( 2[\sin A + \sin B + \sin C] \).