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AP EAMCET · Maths · Trigonometric Ratios & Identities

If \(\sec (\theta+\alpha), \sec \theta, \sec (\theta-\alpha)\) are in arithmetic progression, then \(\cos \theta \cdot \sec \frac{\alpha}{2}=\)


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

Answer & Solution

Correct Answer

(D) \(\pm \sqrt{2}\)

Step-by-step Solution

Detailed explanation

\(2 \sec \theta = \sec (\theta+\alpha) + \sec (\theta-\alpha)\) \(\frac{2}{\cos \theta} = \frac{\cos (\theta-\alpha) + \cos (\theta+\alpha)}{\cos (\theta+\alpha) \cos (\theta-\alpha)}\)…