find the equation of the normal to the curve x=cost y=sint at t=pi/4

We need to find the slope of the line

dy/dx =   dy/dt  /  dx/dt  =  cost / - sin t  =   - cot t

At  t = pi/4, the slope is    - cot (pi/4)  =  - 1

The normal line will have a slope of 1

The point is given by   ( cos pi/4, sin pi/4) =  (  sqrt (2)/2, sqrt (2)/2 )

So....the equation of the tangent lne is

y = 1 (x - sqrt (2) /2 )  +  sqrt(2)/2 

y =  x

Here's the  graph :