The value of 'a' for which $ax^2 +sin^{-1}(x^2 -2x+2) +cos^{-1} (x^2-2x+2) = 0 $ has a real solution, is

$\frac{\pi}{2}$ $-\frac{\pi}{2}$ $\frac{2}{\pi}$ $-\frac{2}{\pi}$

$-\frac{\pi}{2}$

We have, $x^2 - 2x + 2 = (x -1)^2 + 1 ≥ 1.$ So, yje given equation is meaningful for x =1. Putting x =1, we have $a + sin^{-1}(1) cos^{-1}(1) = 0 ⇒ a = -\frac{\pi}{2}$