For the function f(x)=( cos x)-x+1, x ∈ R, between the following two statements (S1) f(x)=0 for only one value of x in [0, π]. (S2) f(x) is…

For the function $\displaystyle f(x)=(\cos x)-x+1, x \in \mathbb{R}$, between the following two statements (S1) $\displaystyle f(x)=0$ for only one value of $\displaystyle x$ in $\displaystyle [0, \pi]$. (S2) $\displaystyle f(x)$ is decreasing in $\displaystyle \left[0, \frac{\pi}{2}\right]$ and increasing in $\displaystyle \left[\frac{\pi}{2}, \pi\right]$.