The value of `a` for which `a x^2+sin^(-1)(x^2-2x+2)+cos^(-1)(x^2-2x+2)=0` has a real solution is `pi/2` (b) `-pi/2` (c) `2/pi` (d) `-2/pi`

Explanation

`ax^2 + sin^-1(x^2-2x+2) + cos^-1(x^2-2x+2) = 0`

`=>ax^2 + sin^-1((x-1)^2 + 1) + cos^-1((x-1)^2 + 1) = 0`

Now, maximum value of `sin^-1 y and cos^-1 y` is `1`.

`:. (x-1)^2 ` should be `0`.

`=> x = 1`

If we put `x = 1` in the given equation,

`a+sin^-1(1)+cos^-1(1) = 0`

`=> a+pi/2+0 = 0`

...