A) \[2n\pi -\frac{\pi }{4}\]
B) \[2n\pi +\frac{\pi }{2}\]
C) \[2n\pi -\frac{\pi }{2}\]
D) \[n\pi \]
Correct Answer: B
Solution :
| \[{{\sin }^{3}}\theta +\sin \theta \cos \theta +{{\cos }^{3}}\theta =1\] |
| \[(sin\theta +cos\theta )\,\,(1-sin\theta cos\theta )+sin\,\theta \,\,cos\,\theta -1=1\] |
| \[(1-sin\theta cos\theta )\,\,(\sin \theta +\cos \theta -1)=0\] \[\Rightarrow \sin 2\theta =2(not\,true)\] or \[\cos \left( \theta -\frac{\pi }{4} \right)=\frac{1}{\sqrt{2}}\] |
| \[\theta -\frac{\pi }{4}=2n\pi \pm \frac{\pi }{4}\]\[\Rightarrow \theta =2n\pi \] or \[\theta =2n\pi +\frac{\pi }{2}\] |
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