Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

For the function $f(x)=(\cos x)-x+1$, where $x\in \mathbb{R}$:

Consider the following two statements:

(S1) The equation $f(x)=0$ has only one solution for $x$ in the interval $[0,\pi ]$.

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