A) 0
B) 1
C) 2
D) 4
Correct Answer: D
Solution :
\[\frac{1}{\sin 10{}^\circ }-\frac{\sqrt{3}}{\cos 10{}^\circ }\] \[=\frac{2\,\left( \frac{1}{2}\cos {{10}^{o}}-\frac{\sqrt{3}}{2}\sin {{10}^{o}} \right)}{\frac{2}{2}\,\left( =\frac{\cos {{10}^{o}}-\sqrt{3}\sin {{10}^{o}}}{\sin {{10}^{o}}\cos {{10}^{o}}}\sin {{10}^{o}}\cos {{10}^{o}} \right)}\] \[=\frac{4\,\sin \,({{30}^{o}}-{{10}^{o}})}{\sin \,{{20}^{o}}}=\frac{4\,\sin \,{{20}^{o}}}{\sin \,{{20}^{o}}}=4\].
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