A) \[\frac{5}{3}\]
B) \[\frac{3}{5}\]
C) \[\frac{2}{5}\]
D) \[\frac{4}{5}\]
Correct Answer: B
Solution :
| [b]\[\cos ec\,\theta -\cot \theta =\frac{1}{2}\] ...(1) |
| Also,\[\cos e{{c}^{2}}\,\theta -{{\cot }^{2}}\theta =1\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\cos ec\theta +\cot \theta =2\] |
| From eqs. (1) and (2). we get |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,2\cos ec\theta =\frac{5}{2}\,\,\,\,\,\,\,\,\Rightarrow \,\,\cos ec\theta =\frac{5}{4}\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\sin \theta =\frac{4}{5}\,\,\,\,\,\,\,\,\Rightarrow \,\,\cos \theta =\sqrt{1-{{\sin }^{2}}\theta }\] |
| \[=\sqrt{1-{{\left( \frac{4}{5} \right)}^{2}}}=\sqrt{1-\frac{16}{25}}=\frac{3}{5}\] |
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