A) \[\frac{\sqrt{3}}{2}\]
B) \[\frac{2\sqrt{3}}{3}\]
C) \[\frac{4\sqrt{3}}{3}\]
D) \[\sqrt{3}\]
Correct Answer: B
Solution :
\[\frac{\sin 30{}^\circ -\cos 60{}^\circ +\tan 45{}^\circ }{\cos 30{}^\circ -\tan 45{}^\circ +\sin 90{}^\circ }\] \[=\frac{\left( \frac{1}{2}-\frac{1}{2}+1 \right)}{\left( \frac{\sqrt{3}}{2}-1+1 \right)}=\frac{2}{\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3}}=\frac{2\sqrt{3}}{3}\]
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