A) \[45{}^\circ \]
B) \[60{}^\circ \]
C) \[90{}^\circ \]
D) \[30{}^\circ \]
Correct Answer: A
Solution :
\[tan\text{ }\theta +cot\text{ }\theta =2\] \[\Rightarrow \tan \,\theta +\frac{1}{\tan \theta }=2\] \[\Rightarrow \frac{{{\tan }^{2}}\theta +1}{\tan \theta }=2\] \[\Rightarrow {{\tan }^{2}}\theta +1=2\tan \theta \] \[\Rightarrow {{\tan }^{2}}\theta -2\tan \theta +1=0\] \[\Rightarrow {{(\tan \theta -1)}^{2}}=0\] \[\Rightarrow \tan \theta -1=0\] \[\Rightarrow \tan \theta =1=\tan 45{}^\circ \] \[\Rightarrow \theta =45{}^\circ \]
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