A) \[n\pi +\frac{\pi }{2}\]
B) \[2n\pi -\frac{\pi }{2}\]
C) \[2n\pi +\frac{\pi }{2}\]
D) None of these
Correct Answer: C
Solution :
\[\frac{1}{\sin \theta }=1+\frac{\cos \theta }{\sin \theta }\Rightarrow \sin \theta +\cos \theta =1\] \[\Rightarrow \] \[\cos \left( \theta -\frac{\pi }{4} \right)\,=\cos \frac{\pi }{4}\Rightarrow \theta -\frac{\pi }{4}=2n\pi \pm \frac{\pi }{4}\] Hence\[\theta =2n\pi \] or\[\theta =2n\pi +\frac{\pi }{2}\]. But \[\theta =2n\pi \] is ruled out.
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