If cos^ - 1 | x| ≥ sin^ - 1 | x| , then the number of integral...

If cos^{- 1}\left|x\right| \ge sin^{- 1} \left|x\right|$,~then$x \in \left[- \dfrac{1}{\sqrt{2}}, \dfrac{1}{\sqrt{2}}\right] {using graph}

For given inequality, we must have $sin x \in \left[- \dfrac{1}{2}, \dfrac{1}{2}\right]$

$⇒ x \in \left[n\pi - \dfrac{π}{4}, n\pi + \dfrac{π}{4}\right], n \in Ι$
Possible integral values of $x$ are $0,3, 6,7, 9$