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
- A \(0\)
- B \(1\)
- C \(2\)
- D \(3\)
Answer & Solution
Correct Answer
(B) \(1\)
Step-by-step Solution
Detailed explanation
We have, \(A+B+C=\pi\) \(\Rightarrow \quad A+B=\pi-C\) \(\Rightarrow \quad \frac{A}{2}+\frac{B}{2}=\frac{\pi}{2}-\frac{C}{2}\) \(\Rightarrow \quad \tan \left(\frac{A}{2}+\frac{B}{2}\right)=\tan \left(\frac{\pi}{2}-\frac{C}{2}\right)\)…
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