A) \[\frac{1}{2}\]
B) \[\frac{\sqrt{3}}{2}\]
C) \[\frac{3\sqrt{3}}{4}\]
D) \[\sqrt{3}\]
Correct Answer: B
Solution :
\[\frac{{{\cot }^{2}}{{15}^{o}}-1}{{{\cot }^{2}}{{15}^{o}}+1}=\frac{\frac{{{\cos }^{2}}{{15}^{o}}}{{{\sin }^{2}}{{15}^{o}}}-1}{\frac{{{\cos }^{2}}{{15}^{o}}}{{{\sin }^{2}}{{15}^{o}}}+1}\] \[=\frac{{{\cos }^{2}}{{15}^{o}}-{{\sin }^{2}}{{15}^{o}}}{{{\cos }^{2}}{{15}^{o}}+{{\sin }^{2}}{{15}^{o}}}=\cos ({{30}^{o}})=\frac{\sqrt{3}}{2}\].
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