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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 \(\fr...

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 cot C2\frac { \mathrm { 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 ) } }

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