$\text{ Consider the following statements }S\text{ and }R\text{. }$

$S:\text{ Both }\sin x\text{ and }\cos x\text{ are decreasing functions in }\left(\frac{\pi }{2},\pi \right)$

$R\underset{\_}{\underset{\_}{\text{ If }}}\text{ a differentiable function decreases in an interval }(a,b),\text{ then its derivative }$$\text{ also decreases in }(a,b)\text{. }$

Which of the following is true?

• A

  $\text{ both }S\text{ and }R\text{ are wrong }$

• B

  $\text{ both }S\text{ and }R\text{ are correct, but }R\text{ is not the correct explanation for }S$

• C

  $\text{ Sis correct and }R\text{ is the correct explanation for }S$

• D

  $S\text{ is correct and }R\text{ is wrong }$