The values of $x$ satisfying the equation ${sin}^{- 1} (x^{2} - 5 x + 7) = 2 {tan}^{- 1} 1$ is (are)

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Solution

The correct options are
A 2
D 3
Given, ${sin}^{- 1} (x^{2} - 5 x + 7) = 2 {tan}^{- 1} 1 = 2. \frac{π}{4} = \frac{π}{2}$
${sin}^{- 1} (x^{2} - 5 x + 7) = {sin}^{- 1} 1$
$x^{2} - 5 x + 7 = 1$
$x^{2} - 5 x + 6 = 0$
$x = 2, 3$
options (A) & (B) are correct.

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