A) \[\frac{1}{\sqrt{3}}\]
B) \[1\]
C) \[\sqrt{3}\]
D) \[\infty \]
Correct Answer: B
Solution :
Given, \[\sin \theta +\cos \theta =\sqrt{2}\] or \[\sin \theta .\frac{1}{\sqrt{2}}+\cos \theta .\frac{1}{\sqrt{2}}=1\] or \[\sin \theta \,\cos {{45}^{o}}+\cos \theta sin{{45}^{o}}=1\] or \[\sin (\theta +{{45}^{o}})=1=\sin {{90}^{o}}\] or \[\theta +{{45}^{o}}={{90}^{o}}\] or \[\theta ={{45}^{o}}\] \[\therefore \] \[\tan \theta =\tan {{45}^{o}}=1\]
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