A) \[2\]
B) \[\frac{2\sin {{20}^{o}}}{\sin {{40}^{o}}}\]
C) \[4\]
D) \[\frac{4\sin {{20}^{o}}}{\sin {{40}^{o}}}\]
Correct Answer: C
Solution :
\[\sqrt{3}\cos ec{{20}^{o}}-\sec {{20}^{o}}\] \[=\tan {{60}^{o}}\cos ec{{20}^{o}}-\sec {{20}^{o}}\] \[=\frac{\sin {{60}^{o}}\cos {{20}^{o}}-\cos {{60}^{o}}\sin {{20}^{o}}}{\cos {{60}^{o}}\sin {{20}^{o}}\cos {{20}^{o}}}\] \[=\frac{\sin ({{60}^{o}}-{{20}^{o}})}{\cos {{60}^{o}}\sin {{20}^{o}}\cos {{20}^{o}}}\] \[=\frac{\sin {{40}^{o}}}{\frac{1}{2}\sin {{20}^{o}}\cos {{20}^{o}}}\] \[=\frac{2\sin {{20}^{o}}\cos {{20}^{o}}}{\frac{1}{2}\sin {{20}^{o}}\cos {{20}^{o}}}=4\]
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