A) \[\cot 7\frac{{{1}^{o}}}{2}\]
B) \[\sin 7\frac{{{1}^{o}}}{2}\]
C) \[\sin \,{{15}^{o}}\]
D) \[\cos \,\,{{15}^{o}}\]
Correct Answer: A
Solution :
We have \[\cot A=\frac{\cos A}{\sin A}=\frac{2{{\cos }^{2}}A}{2\sin A\cos A}=\frac{1+\cos 2A}{\sin 2A}\] Putting \[A=7\frac{{{1}^{o}}}{2}\Rightarrow \cot 7\frac{{{1}^{o}}}{2}=\frac{1+\cos {{15}^{o}}}{\sin {{15}^{o}}}\] On simplification, we get \[\cot 7\frac{{{1}^{o}}}{2}=\sqrt{6}+\sqrt{2}+\sqrt{3}+\sqrt{4}\].
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