A) \[{{15}^{o}}\]or\[{{0}^{o}}\]
B) \[{{30}^{o}}\]or\[{{0}^{o}}\]
C) \[{{45}^{o}}\]or\[{{0}^{o}}\]
D) \[{{60}^{o}}\]or\[{{0}^{o}}\]
Correct Answer: D
Solution :
\[{{\tan }^{2}}\theta +3=3\sec \theta \] \[\Rightarrow \]\[{{\sec }^{2}}\theta -1+3=3\sec \theta \] \[\Rightarrow \]\[{{\sec }^{2}}\theta -3\sec \theta +2=0\] \[\Rightarrow \]\[{{\sec }^{2}}\theta -2\sec \theta -\sec \theta +2=0\] \[\Rightarrow \]\[\sec \theta (\sec \theta -2)-1(\sec \theta -2)=0\] \[\Rightarrow \]\[(\sec \theta -2)(\sec \theta -1)=0\] \[\Rightarrow \]\[\sec \theta =2\]or\[1\] \[\Rightarrow \]\[\theta ={{60}^{o}}\]or\[{{0}^{o}}\].
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