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AP EAMCET · Maths · Trigonometric Ratios & Identities

If A. B. C are the angles of a triangle, then
\(\frac{\sin A+\sin B+\sin C}{\sin ^2 \frac{A}{2}-\sin ^2 \frac{B}{2}+\sin ^2 \frac{C}{2}-1}=\)

  1. A \(-2 \tan \frac{B}{2}\)
  2. B \(-2 \cot \frac{B}{2}\)
  3. C \(2 \tan \frac{B}{2}\)
  4. D \(2 \cot \frac{B}{2}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(-2 \cot \frac{B}{2}\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \frac{\sin A+\sin B+\sin C}{\sin ^2 \frac{A}{2}-\sin ^2 \frac{B}{2}+\sin ^2 \frac{C}{2}-1} \\ = & \frac{2 \sin \frac{A+B}{2} \cdot \cos \frac{A-B}{2}+2 \sin \frac{C}{2} \cdot \cos \frac{C}{2}}{\sin \left(\frac{A+B}{2}\right) \sin \left(\frac{A-B}{2}\right)-\cos…