Q55 / 120 · VITEEE 2010 · Mathematics

The principal value of $\sin -1\left\{\sin \frac{5 \pi}{6}\right\}$ is

  • Correct answer
    A
    $\frac{\pi}{6}$
  • B
    $\frac{5 \pi}{6}$
  • C
    $\frac{7 \pi}{6}$
  • D
    None of these

Solution

$$ \begin{array}{l} \begin{aligned} \sin ^{-1}\left\{\sin \frac{5 \pi}{6}\right\}=& \sin ^{-1}\left\{\sin \left(\pi-\frac{\pi}{6}\right)\right\} \\ &=\sin ^{-1}\left\{\sin \frac{\pi}{6}\right\} \\ &[\because \text { Principal value } \in[0, \pi / 2]] \\ =& \frac{\pi}{6} \end{aligned} \end{array} $$ which is the required principal value.

Hence, the correct answer is option: 'A'.

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