A) \[\frac{\pi }{4}\]
B) \[\frac{\pi }{3}\]
C) \[\frac{2\pi }{3}\]
D) \[\frac{\pi }{2}\]
Correct Answer: A
Solution :
\[\sin \theta +\cos \theta =\sqrt{2}\] Squaring both sides, \[{{\sin }^{2}}\theta +{{\cos }^{2}}\theta +2\sin \theta \cos \theta =2\] \[\Rightarrow \] \[2\sin \theta \cos \theta =1\] \[\Rightarrow \] \[\sin \theta \cos \theta =1\] \[\Rightarrow \] \[\sin \theta .cos\theta =\frac{1}{\sqrt{2}}.\frac{1}{\sqrt{2}}\] \[\Rightarrow \] \[\theta =\frac{\pi }{4}\]
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