Let the functions " f " and " g " be \(\mathrm{f}:\left[0, \frac{\pi}{2}\right] \rightarrow \mathrm{R}\) given by \(\mathrm{f}(\mathrm{x})=\sin \mathrm{x}\) and \(\mathrm{g}:\left[0, \frac{\pi}{2}\right] \rightarrow \mathrm{R}\) given by \(g(x)=\cos x\), where \(R\) is the set of real numbers
Consider the following statements:
Statement (I): f and g are one-one
Statement (II): \(\mathrm{f}+\mathrm{g}\) is one-one
Which of the following is correct?

\(\begin{aligned}
& \mathrm{f}: \text { one }- \text { one }\left[0, \frac{\pi}{2}\right] \rightarrow \text { R.f }(\mathrm{x})=\sin \mathrm{x} \\
& \mathrm{~g}: \text { one }- \text { one }\left[0, \frac{\pi}{2}\right] \rightarrow \text { R.f }(\mathrm{x})=\cos \mathrm{x}
\end{aligned}\)

Statement I is true
\(\begin{aligned}
& (\mathrm{f}+\mathrm{g}):\left[0, \frac{\pi}{2}\right] \rightarrow \mathrm{R} \\
& \mathrm{f}+\mathrm{g}(\mathrm{x})=\sin \mathrm{x}+\cos \mathrm{x} \\
& \left.\begin{array}{l}
\mathrm({f}+\mathrm{g})(0)=0 \\
(\mathrm{f}+\mathrm{g})(\pi / 2)=0
\end{array}\right\} \Rightarrow \mathrm{f}+\mathrm{g} \text { is not one }- \text { one }
\end{aligned}\)