AP EAMCET · Maths · Trigonometric Ratios & Identities
If \(\cos (\theta-\alpha), \cos \theta\) and \(\cos (\theta+\alpha)\) are in harmonic progressions, then \(2 \tan ^2 \theta=\)
- A \(\tan ^2 \frac{\alpha}{2}-1\)
- B \(1+\tan ^2 \frac{\alpha}{2}\)
- C \(1+\cot ^2 \frac{\alpha}{2}\)
- D \(1-\cot ^2 \frac{\alpha}{2}\)
Answer & Solution
Correct Answer
(A) \(\tan ^2 \frac{\alpha}{2}-1\)
Step-by-step Solution
Detailed explanation
Given, \(\cos (\theta-\alpha), \cos \theta\) and \(\cos (\theta+\alpha\) ) are in harmonic progression \(\therefore \quad \frac{2}{\cos \theta}=\frac{\cos (\theta+\alpha)+\cos (\theta-\alpha)}{\cos (\theta-\alpha) \cos (\theta+\alpha)}\)…
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