A) \[n\pi +{{(-1)}^{n}}\frac{\pi }{4}\]
B) \[{{(-1)}^{n}}\frac{\pi }{4}-\frac{\pi }{3}\]
C) \[n\pi +\frac{\pi }{4}-\frac{\pi }{3}\]
D) \[n\pi +{{(-1)}^{n}}\frac{\pi }{4}-\frac{\pi }{3}\]
Correct Answer: D
Solution :
\[\frac{\sqrt{3}}{2}\cos \theta +\frac{1}{2}\sin \theta =\frac{\sqrt{2}}{2}\]{dividing by \[\sqrt{{{(\sqrt{3})}^{2}}+{{1}^{2}}}=2\}\] \[\Rightarrow \] \[\sin \left( \theta +\frac{\pi }{3} \right)=\frac{1}{\sqrt{2}}=\sin \left( \frac{\pi }{4} \right)\] \[\Rightarrow \] \[\theta =n\pi +{{(-1)}^{n}}\frac{\pi }{4}-\frac{\pi }{3}\].
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