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COMEDK · Maths · 8. Trigonometric Ratios & Identities

If \(\sqrt{\frac{1+\cos A}{1-\cos A}}=\frac{x}{y}\), then the value of \(\tan A=\)

  1. A \(\frac{x^{2}+y^{2}}{x^{2}-y^{2}}\)
  2. B \(\frac{2 x y}{x^{2}+y^{2}}\)
  3. C \(\frac{2 x y}{x^{2}-y^{2}}\)
  4. D \(\frac{2 x y}{y^{2}-x^{2}}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{2 x y}{x^{2}-y^{2}}\)

Step-by-step Solution

Detailed explanation

We have, \(\sqrt{\frac{1+\cos A}{1-\cos A}}=\frac{x}{y}\) \(\Rightarrow \sqrt{\frac{2 \cos ^{2} \frac{A}{2}}{2 \sin ^{2} \frac{A}{2}}}=\frac{x}{y}\) \(\Rightarrow \quad \cot \frac{A}{2}=\frac{x}{y} \Rightarrow \tan \frac{A}{2}=\frac{y}{x}\) Now,…