A) \[\frac{1}{5}\]
B) \[\frac{2}{5}\]
C) \[\frac{3}{5}\]
D) \[\frac{5}{3}\]
Correct Answer: C
Solution :
| [c] We have, \[\cot \theta =\frac{1}{\sqrt{3}}\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\theta =60{}^\circ \]\[\left[ \cot 60{}^\circ =\frac{1}{\sqrt{3}} \right]\] |
| \[\therefore \,\,\,\,\frac{1-{{\cos }^{2}}\theta }{2-{{\sin }^{2}}\theta }=\frac{1-{{\cos }^{2}}60{}^\circ }{2-{{\sin }^{2}}60{}^\circ }\] |
| \[=\frac{1-{{\left( \frac{1}{2} \right)}^{2}}}{2-{{\left( \frac{\sqrt{3}}{2} \right)}^{2}}}=\frac{1-\frac{1}{4}}{2-\frac{3}{4}}=\frac{\frac{4-1}{4}}{\frac{8-3}{4}}=\frac{3}{5}\] |
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