Question

Fill in the blanks so that the following statements are correct.
The maximum distance of a point on the graph of the function $y=\sqrt{3}\sin x+\cos x$ from $x-$axis is .............

Answer 1

We have,
$y=\sqrt{3}\sin x+\cos x=2[\frac{\sqrt{3}}{2}\sin x+\frac{1}{2}\cos x]$
$=2\left[\cos \right(\pi /6)\sin x+\sin (\pi /6\left)\cos x\right]$
$=2\sin (x+\pi /6)$
$\therefore$ Max. value of $y=2$. or max. distance from $x-$axis is $2$.