Answer
tangent $y=-x+\pi/2+1$
normal $y=x-\pi/2+1$
See graph.
Work Step by Step
Step 1. Given $y=1+cos(x)$, we have $y'=-sin(x)$ which gives the slope of tangent lines to the curve.
Step 2. At point $(\pi/2,1)$, the slope is $m=y'=-sin(\pi/2)=-1$ and the tangent line equation is $y-1=-1(x-\pi/2)$ or $y=-x+\pi/2+1$
Step 3. Its normal will have a slope $n=-1/m=1$, and the equation will be $y-1=1(x-\pi/2)$ or $y=x-\pi/2+1$
Step 4. See graph.
