Answer
The tangent line at $ x=0$ is given by
$$ y=1.$$
Work Step by Step
Since $ y=x^3+\cos x $, then the slope at $ x=0$ is given as follows
$$ y'=3x^2-\sin x\Longrightarrow m=y'(0)=0.$$
The equation of the tangent line at $ x=0$ is given by
$$ y=(0)x+c=c.$$
To find $ c $ we use the fact that the tangent line and the curve coincide at $ x=0$, so we have
$ y(0)=1=c $. Hence the equaion of the tangent line at $ x=0$ is given by
$$ y=1.$$
