Question

Find the maximum value of $\sqrt{3}\sin x+\cos x$ .

Answer 1

$\sqrt{3}\sin x+\cos x=2(\frac{\sqrt{3}}{2}\sin x+\frac{1}{2}\sin x)=2\sin (x+\frac{\pi }{6})$
which is maximum when $x+\pi /6=\pi /2$ or $x={60}^0$ and has maximum value 2
Ans: 2