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Inverse Trigonometric Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsInverse Trigonometric Functions1 Mark
MCQ
$\tan^{-1}\frac{1}{11}+\tan^{-1}\frac{2}{11}$ is equal to:
  • A
    $0$
  • B
    $\frac{1}{2}$
  • C
    $-1$
  • ✓
    None of these
✓

Answer

Correct option: D.
None of these
$\tan^{-1}\frac{1}{11}+\tan^{-1}\frac{2}{11}$
$=\tan^{-1}\Bigg(\frac{\frac{1}{11}+\frac{2}{11}}{1-\frac{2}{11}\times\frac{1}{11}}\Bigg)$
$=\tan^{-1}\Bigg(\frac{\frac{3}{11}}{1-\frac{2}{121}}\Bigg)$
$=\tan^{-1}\Big(\frac{33}{119}\Big)$

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