Question

In a triangle \(ABC\), if \[ \tan\frac{A}{2}:\tan\frac{B}{2}:\tan\frac{C}{2}=1:2:3, \] then \[ \frac{a+3c}{b}= \]

• A. \(4\)
• B. \(3\)
• C. \(2\)
• D. \(6\)

Hint:

For triangle problems involving \(\tan\frac A2,\tan\frac B2,\tan\frac C2\), remember: \[ \tan\frac A2:\tan\frac B2:\tan\frac C2 = \frac1{s-a}:\frac1{s-b}:\frac1{s-c}. \] This converts trigonometric ratios directly into side relations.

Answer 1

The Correct Option is A