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Inverse Trigonometric Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsInverse Trigonometric Functions1 Mark
MCQ
$\tan ^{-1} 3+\tan ^{-1} \lambda=\tan ^{-1}\left(\frac{3+\lambda}{1-3 \lambda}\right)$ is valid for what values of $\lambda$ ?
  • A
    $\quad \lambda \in\left(-\frac{1}{3}, \frac{1}{3}\right)$
  • B
    $\lambda>\frac{1}{3}$
  • C
    $\quad \lambda<\frac{1}{3}$
  • D
    All real values of $\lambda$
✓

Answer

$\begin{array}{l}\text {Given, } \tan ^{-1} 3+\tan ^{-1} \lambda=\tan ^{-1}\left(\frac{3+\lambda}{1-3 \lambda}\right) \\ \tan ^{-1} 3+\tan ^{-1} \lambda=\tan ^{-1}\left(\frac{3+\lambda}{1-3 \lambda}\right) \text { for } 3 \lambda<1 \\ \therefore \quad 3 \lambda<1 \Rightarrow \lambda<\frac{1}{3}\end{array}$

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