A) \[\sqrt{2}\]
B) \[\sqrt{3}\]
C) 2
D) 4
E) \[\sqrt{5}\]
Correct Answer: D
Solution :
\[\frac{\sin 80{}^\circ -\cos 80{}^\circ \sqrt{3}}{\sin 80{}^\circ \cos 80{}^\circ }\] \[=\frac{2\left[ \frac{1}{2}\sin 80{}^\circ -\frac{\sqrt{3}}{2}\cos 80{}^\circ \right]}{\sin 80{}^\circ \cos 80{}^\circ }\] \[=\frac{4[\sin (80{}^\circ -60{}^\circ )]}{2\sin 80{}^\circ \cos 80{}^\circ }\] \[=\frac{4\sin 20{}^\circ }{2\sin 80{}^\circ }=\frac{4\sin 20{}^\circ }{\sin (\pi -20{}^\circ )}=4\]
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