A) \[x=2n\pi \,;\,n=0,\pm 1,\pm 2...\]
B) \[x=2n\pi \,+\pi \,/2;n=0,\pm 1,\pm 2...\]
C) \[x=n\pi \,+{{(-1)}^{n}}\underset{n=0,\pm 1,\pm 2...}{\mathop{\frac{\pi }{4}-\frac{\pi }{4}}}\,\]
D) None of these
Correct Answer: C
Solution :
| \[\sin x+\cos \,x=1\]\[\Rightarrow \]\[\frac{1}{\sqrt{2}}\sin \,x+\frac{1}{\sqrt{2}}\cos =\frac{1}{\sqrt{2}}\] |
| \[\Rightarrow \]\[\sin \,x\cos \frac{\pi }{4}+\cos \,x\sin \frac{\pi }{4}=\sin \frac{\pi }{4}\] |
| \[\Rightarrow \]\[\sin \,(x+\pi /4)=\sin \pi /4\] \[\Rightarrow \]\[x+\pi /4=n\pi +{{(-1)}^{n}}\pi /4,n\in Z\] |
| \[\Rightarrow \]\[x+\pi /4=n\pi +{{(-1)}^{n}}\pi /4-\pi /4\] |
| Where n=0, \[\pm 1,\pm 2....\] |
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