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TS EAMCET · Maths · Trigonometric Ratios & Identities

If \(\cos \left(\frac{\alpha-\beta}{2}\right)=2 \cos \left(\frac{\alpha+\beta}{2}\right)\), then \(\tan \frac{\alpha}{2} \tan \frac{\beta}{2}=\)

  1. A \(\frac{1}{2}\)
  2. B \(\frac{1}{4}\)
  3. C \(\frac{1}{3}\)
  4. D \(\frac{1}{8}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{1}{3}\)

Step-by-step Solution

Detailed explanation

Given, \(\cos \left(\frac{\alpha-\beta}{2}\right)=2 \cos \left(\frac{\alpha+\beta}{2}\right)\) \(\therefore \quad \frac{\cos \left(\frac{\alpha-\beta}{2}\right)}{\cos \left(\frac{\alpha+\beta}{2}\right)}=\frac{2}{1}\) Now, using componendo and dividendo,…