A) 1
B) \[\frac{1}{\sqrt{2}}\]
C) \[\sqrt{2}\]
D) \[\frac{\sqrt{3}}{2}\]
Correct Answer: C
Solution :
Given, \[\tan \theta +\frac{1}{\tan \theta }=2\] \[\Rightarrow \,\,{{\tan }^{2}}\theta +1=2\tan \theta \] \[\Rightarrow \,\,{{\tan }^{2}}\theta -2\tan \theta +1=0\] \[\Rightarrow \,\,{{\left( \tan \theta -1 \right)}^{2}}=0\] \[\Rightarrow \,\tan \theta =1\] \[\Rightarrow \,\,\tan \theta =\tan 45{}^\circ \] \[\Rightarrow \,\,\theta =45{}^\circ \] \[\Rightarrow \,\,\cos ec\,45{}^\circ =\sqrt{2}\]
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