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AP EAMCET · Maths · Trigonometric Ratios & Identities

If two acute angles \(A\) and \(B\) are such that \(A \neq B\) and \(\frac{x}{y}=\frac{\cos A}{\cos B}\), then \(\frac{x \tan A-y \tan B}{x+y}=\)

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

Answer & Solution

Correct Answer

(A) \(\tan \left(\frac{\mathrm{A}-\mathrm{B}}{2}\right)\)

Step-by-step Solution

Detailed explanation

Given : \(\frac{x}{y}=\frac{\cos A}{\cos B}\) \(\frac{x \tan A-y \tan B}{x+y}=\frac{\frac{x}{y} \tan A-\tan B}{\frac{x}{y}+1}\) \(=\frac{\frac{\cos A}{\cos B} \cdot \tan A-\tan B}{\frac{\cos A}{\cos B}+1}\)…