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Question: If a, b, c are the sides of a triangle ABC and 3a = b + c, then cot \(\frac{1}{2}\)B cot \(\frac{1}{...

If a, b, c are the sides of a triangle ABC and 3a = b + c, then cot 12\frac{1}{2}B cot 12\frac{1}{2}C is-

A

1

B

3\sqrt{3}

C

2

D

2\sqrt{2}

Answer

2

Explanation

Solution

cot B2\frac{B}{2}cot C2\frac{C}{2}= s(s−b)(s−a)(s−c)s(s−c)(s−a)(s−b)\sqrt{\frac{s(s - b)}{(s - a)(s - c)}\frac{s(s - c)}{(s - a)(s - b)}}

= ss−a\frac{s}{s - a}=2s2s−2a\frac{2s}{2s - 2a}= a+b+cb+c−a\frac{a + b + c}{b + c - a}= a+3a3a−a\frac{a + 3a}{3a - a}= 2