JEE Math Practice Question

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 $$\left[\frac{\pi}{2}, \pi\right]$$.

1. A.Both (S1) and (S2) are incorrect.
2. B.Only (S1) is correct.
3. C.Only (S2) is correct.
4. D.Both (S1) and (S2) are correct.