A) 3
B) 5
C) 4
D) None of these
Correct Answer: C
Solution :
\[1+\sin \left( \frac{\pi }{4}+\theta \right)+2\cos \left( \frac{\pi }{4}-\theta \right)\] \[=1+\frac{1}{\sqrt{2}}(\cos \theta +\sin \theta )+\sqrt{2}(\cos \theta +\sin \theta )\] \[=1+\left( \frac{1}{\sqrt{2}}+\sqrt{2} \right).(\cos \theta +\sin \theta )\] \[=1+\left( \frac{1}{\sqrt{2}}+\sqrt{2} \right).\sqrt{2}\cos \left( \theta -\frac{\pi }{4} \right)\] \[\therefore \]Maximum value\[=1+\left( \frac{1}{\sqrt{2}}+\sqrt{2} \right).\sqrt{2}=4\]
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