Answer
The equation of the tangent line at $ x=0$ is given by
$$ y=x+3.$$
Work Step by Step
Since $ y=\sin x+3\cos x $, then the slope at $ x=0$ is given as follows
$$ y'=\cos x-3\sin x \Longrightarrow m=y'(0)=1.$$
The equation of the tangent line at $ x=0$ is given by
$$ y= x+c.$$
To find $ c $, we use the fact that the tangent line and the curve coincide at $ x=0$; so we have
$ y(0)=3 =c $. Hence the equation of the tangent line at $ x=0$ is given by
$$ y=x+3.$$
