Application Of Derivatives

For the function \(f(x)=(\cos x)-x+1, x \in \mathbb{R}\), between the following two statements

(S1) \(f(x)=0\) for only one value of \(x\) in \([0, \pi]\).

(S2) \(f(x)\) is decreasing in \(\left[0, \frac{\pi}{2}\right]\) and increasing in \(\left[\frac{\pi}{2}, \pi\right]\).