Question

Find the value of in the equation $|x^2-a|={\cos }^{-1}\left(\cos x\right)$

Answer 1

$|x^2-a|={\cos }^{-1}\left(\cos x\right)$

$\Rightarrow |x^2-a|=x$

$\Rightarrow x^2-a=\pm x$

$\Rightarrow x^2-a=x$,

$\Rightarrow x^2-a=-x$

$\Rightarrow x^2-x-a=0$,

$\Rightarrow x^2+x-a=0$

$a=x^2-x$, $a=+(x^2+x)$

$\therefore a=x^2+x$

(or) $a=x(x\pm 1)$.