A) \[n\pi \]
B) \[n\pi +\frac{\pi }{3}\]
C) \[n\pi -\frac{\pi }{3}\]
D) All of these
Correct Answer: D
Solution :
| Using \[\sec 2\theta =\frac{1}{\cos 2\theta }=\frac{1+{{\tan }^{2}}\theta }{1-{{\tan }^{2}}\theta }\] |
| Given equation is: \[{{\tan }^{2}}\theta +\frac{1+{{\tan }^{2}}\theta }{1-{{\tan }^{2}}\theta }=1\] |
| \[\Rightarrow \,\,\,{{\tan }^{2}}\theta (3-{{\tan }^{2}}\theta )=0\] |
| \[\Rightarrow \,\,\,\tan \theta =0\] or \[\pm \sqrt{3}\] |
| Thus \[\theta =m\pi ,\] \[n\pi \pm \pi /3\] where m and n are integers. |
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