Question:
The maximum value of $3 \cos \theta+5 \sin \left(\theta-\frac{\pi}{6}\right)$ for any real value of $\theta$ is :
Correct Option: 1
Solution:
$y=3 \cos \theta+5\left(\sin \theta \frac{\sqrt{3}}{2}-\cos \theta \frac{1}{2}\right)$
$\frac{5 \sqrt{3}}{2} \sin \theta+\frac{1}{2} \cos \theta$
$\mathrm{y}_{\max }=\sqrt{\frac{75}{4}+\frac{1}{4}}=\sqrt{19}$
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