A) \[\frac{3}{2}\]
B) \[0\]
C) \[\frac{2}{3}\]
D) \[1\]
Correct Answer: D
Solution :
\[\tan \theta +\cot \theta =2,\,\frac{\sin \theta }{\cos \theta }+\frac{\cos \theta }{\sin \theta }=2\] \[\frac{{{\sin }^{2}}\theta +{{\cos }^{2}}\theta }{2\sin \theta .\,cos\theta }=1\,\,\,\,\left[ \because \,\,\,{{\sin }^{2}}\theta +{{\cos }^{2}}\theta =1 \right]\] \[2\sin \theta .\cos \theta =1\,\,\,\,\Rightarrow \,\,\,\sin 2\theta =\underline{\mathbf{1}}\]
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