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?

• Correct answer
  A

  Statement (I) is true, statement (II) is false
• B

  Statement (I) is false, statement (II) is true
• C

  Both statements (I) and (I) are true
• D

  Both statements (I) and (II) are false

Hence, the correct answer is option: 'A'.