A) \[n\pi \]
B) \[2n\pi +\frac{3\pi }{4}\]
C) \[2n\pi \]
D) \[(2n\pi +1)\]
Correct Answer: B
Solution :
Given that, \[\sin x-\cos x=\sqrt{2}\] \[\Rightarrow \] \[\frac{1}{\sqrt{2}}\sin x-\frac{1}{\sqrt{2}}\cos x=1\] \[\Rightarrow \,\,\sin {{45}^{o}}\sin x-\cos {{45}^{o}}\cos x=1\] \[\Rightarrow \] \[\cos \left( x+\frac{\pi }{4} \right)=-1\] \[\Rightarrow \] \[\cos \left( x+\frac{\pi }{4} \right)=\cos \,(\pi )\] \[\Rightarrow \] \[x+\frac{\pi }{4}=2n\pi +\pi \] \[\Rightarrow \] \[x=2n\pi +\frac{3\pi }{4}\]
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