A) \[\sqrt{2}\cos \theta \]
B) \[\sqrt{2}\sin \theta \]
C) \[2\cos \theta \]
D) \[-\sqrt{2}\cos \theta \]
Correct Answer: A
Solution :
We have \[\cos \theta -\sin \theta =\sqrt{2}\,\sin \theta \] \[\Rightarrow \,\cos \theta =(\sqrt{2}+1)\,\sin \theta \,\Rightarrow \,(\sqrt{2}-1)\cos \theta =\sin \theta \] \[\Rightarrow \,\sqrt{2}\,\cos \theta -\cos \theta =\sin \theta \Rightarrow \,\sin \theta +\cos \theta =\sqrt{2}\,\cos \theta .\]
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