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Question: In a DABC <img src="https://cdn.pureessence.tech/canvas_357.png?top_left_x=507&top_left_y=0&width=30...

In a DABC , c=3−1c = \sqrt { 3 } - 1 & ĐA = 600, then the

value of tan⁡12(B−C)\tan \frac { 1 } { 2 } ( B - C ) is

A

2

B

12\frac { 1 } { 2 }

C

1

D

3

Answer

1

Explanation

Solution

tan⁡B−C2=b−cb+ccot⁡A/2\tan \frac { \mathrm { B } - \mathrm { C } } { 2 } = \frac { \mathrm { b } - \mathrm { c } } { \mathrm { b } + \mathrm { c } } \cot \mathrm { A } / 2

= (3+1)−(3−1)(3+1)+(3−1)cot⁡30\frac { ( \sqrt { 3 } + 1 ) - ( \sqrt { 3 } - 1 ) } { ( \sqrt { 3 } + 1 ) + ( \sqrt { 3 } - 1 ) } \cot 30

= 13×3=1\frac { 1 } { \sqrt { 3 } } \times \sqrt { 3 } = 1