A) 1
B) \[\frac{1}{2}\]
C) \[\frac{1}{\sqrt{2}}\]
D) \[\frac{\sqrt{3}}{2}\]
Correct Answer: A
Solution :
Given, \[x\,\tan \,45{}^\circ \,\cos 60{}^\circ =\sin \,60{}^\circ \cot \,60{}^\circ \] We know that, \[\tan \,45{}^\circ =1,\,\cos 60{}^\circ =\frac{1}{2},\,\sin \,60{}^\circ =\frac{\sqrt{3}}{2}\] \[\Rightarrow \,\,\,\cot \,60{}^\circ =\frac{1}{\sqrt{3}}\] \[\Rightarrow \,\,\,\,x\times 1\times \frac{1}{2}=\frac{\sqrt{3}}{2}\times \frac{1}{\sqrt{3}}\] \[\Rightarrow \,\,\,\,x=1\]
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