If $0 \leq \mathrm{A}, \mathrm{B} \leq \frac{\pi}{4}$ and $\cot \mathrm{A}+\cot \mathrm{B}+\tan \mathrm{A}+\tan \mathrm{B}=\cot \mathrm{A} \cot \mathrm{B}-\tan \mathrm{A} \tan \mathrm{B}$ then $\sin (\mathrm{A}+\mathrm{B})=$

• A

  $0$
• B

  $\frac{1}{2}$
• Correct answer
  C

  $\frac{1}{\sqrt{2}}$
• D

  $\frac{\sqrt{3}}{2}$

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