Answer
$y=x+1$
Work Step by Step
Given: $y=(1+x) \cos x$
Apply product rule, we get
$y'=\cos x-(1+x) \sin x$
At $(0, 1)$, we have
$y'=\cos(0)-(1+0) \sin (0)=1$
so we have $m=y'=1$
Formula to tangent line is : $y=mx+b$
$y-y_1=m(x-x_1)$
At $(0, 1)$, we have
$y-1=1(x-0)$
This implies
$y=x+1$