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CUET · MATHS · PYQ PAPER 2023

\(\tan ^{-1} 3+\tan ^{-1} \lambda=\tan ^{-1}\left(\frac{3+\lambda}{1-3 \lambda}\right)\) is valid for which values of \(\lambda\) ?

  1. A \(\lambda \in\left(-\frac{1}{3}, \frac{1}{3}\right)\)
  2. B \(\lambda>\frac{1}{3}\)
  3. C \(\lambda<\frac{1}{3}\)
  4. D All real values of \(\lambda\)
Verified Solution

Answer & Solution

Correct Answer

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

Step-by-step Solution

Detailed explanation

\(\tan ^{-1} x+\tan ^{-1} y=\tan ^{-1}\left(\frac{x+y}{1-xy}\right)\) is valid if \(xy \(3 \cdot \lambda \(\lambda < \frac{1}{3}\)