A) \[2n\pi +\frac{\pi }{4}\]
B) \[(2n+1)\,\pi +\frac{\pi }{4}\]
C) \[n\pi +\frac{\pi }{4}\]
D) \[n\pi \pm \frac{\pi }{4}\]
Correct Answer: B
Solution :
\[\cos \theta =-\frac{1}{\sqrt{2}}\Rightarrow \theta =\frac{3\pi }{4},\,\frac{5\pi }{4}\]; \[\tan \theta =1\Rightarrow \theta =\frac{\pi }{4},\,\frac{5\pi }{4}\] \[\therefore \] The general value is \[2n\pi +\frac{5\pi }{4}\] or \[(2n+1)\pi +\frac{\pi }{4}\].
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