A) \[cos\text{ }60{}^\circ \]
B) \[cos\text{ 3}0{}^\circ \]
C) \[cos\text{ 45}{}^\circ \]
D) \[cos\text{ 75}{}^\circ \]
Correct Answer: B
Solution :
[b] \[a\ge 2b\Rightarrow \frac{b}{a}\le \frac{1}{2}\] \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,{{e}^{2}}=1-\frac{{{b}^{2}}}{{{a}^{2}}}\ge 1-\frac{1}{4}=\frac{3}{4}\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,e\ge \frac{\sqrt{3}}{2}\] \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{e}_{\min }}=\frac{\sqrt{3}}{2}\]
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