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TS EAMCET · Maths · Trigonometric Ratios & Identities

If \(A+B+C=\frac{\pi}{3}\) then \(\sin \left(\frac{\pi-6 A}{6}\right)+\sin \left(\frac{\pi-6 B}{6}\right)+\sin C=\)

  1. A \(-1+4 \cos \left(\frac{\pi-6 A}{12}\right) \cos \left(\frac{\pi-6 B}{12}\right) \sin \frac{C}{2}\)
  2. B \(4 \sin \left(\frac{\pi+6 A}{12}\right) \sin \left(\frac{\pi+6 B}{12}\right) \cos \frac{C}{2}\)
  3. C \(1-4 \cos \left(\frac{\pi-6 A}{12}\right) \cos \left(\frac{\pi-6 B}{12}\right) \cos \frac{\pi-6 C}{12}\)
  4. D \(4 \cos \left(\frac{\pi-6 A}{12}\right) \cos \left(\frac{\pi-6 B}{12}\right) \sin \frac{C}{2}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(4 \cos \left(\frac{\pi-6 A}{12}\right) \cos \left(\frac{\pi-6 B}{12}\right) \sin \frac{C}{2}\)

Step-by-step Solution

Detailed explanation

Given, \(A+B+C=\frac{\pi}{3}\)…