Question

In a triangle \(ABC\), if \(s=\dfrac{15}{2},\; a=3,\; b=5\), then \[ \frac{\sin \dfrac{B}{2}}{\sin \dfrac{A}{2}}= \]

• A. \(\cot\dfrac{C}{2}\)
• B. \(2\sin\dfrac{C}{2}\)
• C. \(2\cosec\dfrac{C}{2}\)
• D. \(\sin\dfrac{C}{2}\)

Hint:

Remember the half-angle formulas in a triangle: \[ \sin\frac{A}{2} = \sqrt{\frac{(s-b)(s-c)}{bc}}, \] \[ \sin\frac{B}{2} = \sqrt{\frac{(s-a)(s-c)}{ac}}, \] \[ \sin\frac{C}{2} = \sqrt{\frac{(s-a)(s-b)}{ab}}. \]

Answer 1

The Correct Option is B