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The set of values of 'a' for which the equation $x^{2} + a x + \sin^{- 1} (x^{2} - 2 x + 2) + \cos^{- 1} (x^{2} - 2 x + 2) = 0$ has at least one real solution is given by

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$(- \infty, - \sqrt{2 π}) \cup (\sqrt{2 π}, \infty)$

$- 1 - \frac{π}{2}$

$(- \infty, - \sqrt{2 π}] \cup [\sqrt{2 π}, \infty)$

answer is D.

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Detailed Solution

$x^{2} - 2 x + 2 = (x - 1)^{2} + 1 \leq 1$
$∴ \cos^{- 1} (x^{2} - 2 x + 2) is defined only for x = 1$
Also, then $1 + a + (\frac{π}{2}) = 0 \Rightarrow a = - 1 - (\frac{π}{2})$

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