In a triangle $\mathrm{ABC}$, if $\tan \left(\frac{A-B}{2}\right)=\frac{1}{3} \tan \left(\frac{A+B}{2}\right)$ then $a: b=$

• Correct answer
  A

  $2: 1$
• B

  $3: 1$
• C

  $4: 1$
• D

  $1: 3$

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