A) \[x=0\]
B) \[y=0\]
C) \[x=y\]
D) \[x=n\pi -\frac{\pi }{4}+y,\,\,(n\in I)\]
Correct Answer: D
Solution :
The expression is equal to \[\sin (x-y)+\cos (x-y)=\sqrt{2}\left\{ \sin \left( \frac{\pi }{4}+x-y \right) \right\}\], which is zero, if \[\sin \left( \frac{\pi }{4}+x-y \right)=0\] i.e., \[\frac{\pi }{4}+x-y=n\pi (n\in I)\Rightarrow x=n\pi -\frac{\pi }{4}+y\].
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