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COMEDK · Maths · 8. Trigonometric Ratios & Identities

If \(A+B+C=180^{\circ}\), then \(\Sigma \tan \frac{A}{2} \tan \frac{B}{2}\) is equal to

  1. A \(0\)
  2. B \(1\)
  3. C \(2\)
  4. D \(3\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(1\)

Step-by-step Solution

Detailed explanation

We have, \(A+B+C=\pi\) \(\Rightarrow \quad A+B=\pi-C\) \(\Rightarrow \quad \frac{A}{2}+\frac{B}{2}=\frac{\pi}{2}-\frac{C}{2}\) \(\Rightarrow \quad \tan \left(\frac{A}{2}+\frac{B}{2}\right)=\tan \left(\frac{\pi}{2}-\frac{C}{2}\right)\)…