A) \[\frac{1}{\sqrt{3}}\]
B) \[\sqrt{3}\]
C) \[1\]
D) \[0\]
Correct Answer: A
Solution :
| [a] Given, \[\sin \alpha =\frac{1}{2}=\sin 30{}^\circ \] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\alpha =30{}^\circ \] |
| and\[\tan \beta =\frac{1}{\sqrt{3}}=\tan 30{}^\circ \] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\beta =30{}^\circ \] |
| \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\cot (\alpha +\beta )=\cot (30{}^\circ +30{}^\circ )=\cot 60{}^\circ =\frac{1}{\sqrt{3}}\] |
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