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Inverse Trigonometric Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsInverse Trigonometric Functions1 Mark
MCQ
The principal value of $\tan ^{-1}\left(\tan \frac{9 \pi}{8}\right)$ :
  • ✓
    $\frac{\pi}{8}$
  • B
    $\frac{3 \pi}{8}$
  • C
    $\frac{-\pi}{8}$
  • D
    $\frac{-3 \pi}{8}$
✓

Answer

Correct option: A.
$\frac{\pi}{8}$
(A)
$
\begin{array}{l}
\tan ^{-1}\left(\tan \frac{9 \pi}{8}\right)=\tan ^{-1}\left[\tan \left(\pi+\frac{\pi}{8}\right)\right] \\
=\tan ^{-1}\left[\tan \frac{\pi}{8}\right]=\frac{\pi}{8}
\end{array}
$
Hence, correct option is (A)

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