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COMEDK · Maths · 8. Trigonometric Ratios & Identities

If \(\cos A=m \cos B\) and \(\cot \left(\dfrac{A+B}{2}\right)=\lambda \tan \left(\dfrac{B-A}{2}\right)\), then \(\lambda\) is equal to

  1. A None of these
  2. B \(\dfrac{m}{m-1}\)
  3. C \(\dfrac{m+1}{m-1}\)
  4. D \(\dfrac{m+1}{m}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\dfrac{m+1}{m-1}\)

Step-by-step Solution

Detailed explanation

Given \(\cos A = m \cos B\), we have \(\dfrac{\cos A}{\cos B} = m\). Applying componendo and dividendo, \(\dfrac{\cos A + \cos B}{\cos A - \cos B} = \dfrac{m+1}{m-1}\). Using the sum-to-product formulas,…