A) \[{{30}^{o}}\]
B) \[{{45}^{o}}\]
C) \[{{75}^{o}}\]
D) \[{{15}^{o}}\]
Correct Answer: A
Solution :
\[\tan \left( \frac{B-C}{2} \right)=\frac{b-c}{b+c}\cot \frac{A}{2}\] Þ \[\tan \left( \frac{90{}^\circ }{2} \right)=\frac{\sqrt{3}-1}{\sqrt{3}+1}\cot \frac{A}{2}\] Þ \[\tan \left( \frac{A}{2} \right)=\frac{\sqrt{3}-1}{\sqrt{3}+1}=\frac{3+1-2\sqrt{3}}{2}=2-\sqrt{3}\] Þ \[\frac{A}{2}={{15}^{o}}\Rightarrow A={{30}^{o}}\].
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