If $f(\sin x) - f(-\sin x) = x^2-1$ is defined for all real x, then the value of $x^2 - 2$ can be ____.
Answer & explanation
We have,
$f(\sin x) - f(-\sin x) = x^2-1$ ...(i)
Replacing x by - x, we get
$f (- \sin x) - f (\sin x) = x^2 -1$ ...(ii)
Adding (i) and (ii), we get
$2(x^2-1)=0⇒ x^2-1=0⇒x^2-2=-1$