A) \[\sqrt{3}\]
B) \[\frac{1}{\sqrt{3}}\]
C) \[\frac{\sqrt{3}}{2}\]
D) \[1\]
Correct Answer: A
Solution :
| [a] Given, \[\sin A=\frac{1}{2}\] |
| \[\cos A=\sqrt{1-{{\sin }^{2}}A}\]\[[{{\sin }^{2}}A+{{\cos }^{2}}A=1]\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\cos A=\sqrt{1-{{\left( \frac{1}{2} \right)}^{2}}}=\sqrt{1-\frac{1}{4}}=\sqrt{\frac{3}{4}}=\frac{\sqrt{3}}{2}\] |
| Now,\[\cot A=\frac{\cos A}{\sin A}=\frac{\sqrt{3}/2}{1/2}=\sqrt{3}\] |
| Hence, the required value of cot A is \[\sqrt{3}\]. |
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