A) \[\frac{2}{\sqrt{3}}\]
B) \[2\sqrt{3}\]
C) \[\sqrt{\frac{2}{3}}\]
D) \[\frac{\sqrt{6}}{12}\]
Correct Answer: D
Solution :
\[\frac{\sin 30{}^\circ \cos 45{}^\circ }{\tan 60{}^\circ }=\frac{\frac{1}{2}\times \frac{1}{\sqrt{2}}}{\sqrt{3}}\] \[=\frac{1}{(2\sqrt{2})(\sqrt{3})}=\frac{1}{(2\sqrt{6})}\frac{\sqrt{6}}{\sqrt{6}}=\frac{\sqrt{6}}{12}\]
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