If $\sin x-\sin y=\frac{27}{65}$ and $\cos x-\cos y=\frac{-21}{65}$, then $\sin (x+y)=$ $\sin \mathrm{x}-\sin \mathrm{y}=\frac{27}{65}$ మరియు $\cos \mathrm{x}-\cos \mathrm{y}=\frac{-21}{65}$ అయితే, $\sin (\mathrm{x}+\mathrm{y})=$

• A

  $-\frac{63}{65}$
• B

  $\frac{16}{65}$
• Correct answer
  C

  $\frac{63}{65}$
• D

  $-\frac{16}{65}$

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