If $x + 1 / x = 5 / 2$ , then the principal value of $\sin^{- 1} x$ is

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$π / 4$

$5 π / 6$

$π / 6$

$π / 3$

answer is A.

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Detailed Solution

$\begin{array}{l} Let y = \sin^{- 1} x \Rightarrow \sin y + \frac{1}{\sin y} = \frac{5}{2} \\ \Rightarrow 2 \sin^{2} y - 5 \sin y + 2 = 0 \\ \Rightarrow \sin y = (1 / 2) \Rightarrow y = \sin^{- 1} (1 / 2) = π / 6 \end{array}$

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