A) \[\frac{\sqrt{79}}{2}\]
B) \[\sqrt{31}\]
C) \[\sqrt{34}\]
D) \[\sqrt{19}\]
Correct Answer: D
Solution :
Let \[x=3\cos \theta +5\sin \left( \theta -\frac{\pi }{6} \right)\] \[=3\cos \theta +5\left( \frac{\sqrt{3}}{2}\sin \theta -\frac{1}{2}\cos \theta \right)\] \[=\frac{5\sqrt{3}}{2}\sin \theta +\frac{1}{2}\cos \theta \] So, maximum value of x for real \[\theta \] is\[\sqrt{\frac{75}{4}+\frac{1}{4}}=\sqrt{19}\]
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