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TS EAMCET · Maths · Trigonometric Ratios & Identities

If \(\tan \beta=\frac{n \sin \alpha \cos \alpha}{1-n \cos ^2 \alpha}\), then \(\tan (\alpha+\beta) \cdot \cot \alpha=\)

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

Answer & Solution

Correct Answer

(A) \(\frac{-1}{n-1}\)

Step-by-step Solution

Detailed explanation

\(\tan \beta=\frac{n \sin \alpha \cos \alpha}{1-n \cos ^2 \alpha}=\frac{n \tan \alpha}{\sec ^2 \alpha-n}=\frac{n \tan \alpha}{(1-n)+\tan ^2 \alpha}\) \(\tan (\alpha+\beta)=\frac{\tan \alpha+\tan \beta}{1-\tan \alpha \tan \beta}\)…