Question

In $ \triangle ABC $, with usual notations, $ \sin \left( \frac{A}{2} \right) \cdot \sin \left( \frac{C}{2} \right) = \sin \left( \frac{B}{2} \right) \quad \text{and} \quad 2s \text{ is the perimeter of the triangle. Find the value of } s. $ Then the value of $ s $ is:

• A. \( 2b \)
• B. \( 6b \)
• C. \( 3b \)
• D. \( 4b \)

Hint:

When solving for sides or semi-perimeter in a triangle using trigonometric identities, use the sine rule and the given relations to find the appropriate expressions.