A) \[\sqrt{2}\]
B) \[90{}^\circ \]
C) \[1\]
D) \[15{}^\circ \]
Correct Answer: D
Solution :
\[\sin 3\phi +\cos 3\phi \] \[=\sqrt{2}\left( \frac{1}{\sqrt{2}}\cos 3\phi +\frac{1}{\sqrt{2}}\sin 3\phi \right)\] \[=\sqrt{2}\,\,(\sin 45{}^\circ \cos 3\phi +\cos 45{}^\circ \sin 3\phi )\] \[=\sqrt{2}\sin (45{}^\circ +3\phi )\] \[\therefore \] The maximum value occurs when \[\sin \,\,(45{}^\circ 3\phi )=1\] \[\therefore \] \[45{}^\circ +3\phi =90{}^\circ \] \[\Rightarrow \] \[\phi =15{}^\circ \]
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