How do you find the equation for the lines that are tangent and normal to the curve #y=1+cosx# at the point #(pi/2, 1)#?
Start with the derivative
This is the slope of the tangent line.
Use the point-slope form of a line to find its equation.
In this case
Solve for y.
The normal is perpendicular to the tangent.
In this case, the normal slope is
Use the same point, and the point-slope form of a line, to obtain the equation of the normal line.