Given curve is y = tan x

Now applying first derivative, we get

This is the slope of the tangent

Substituting (0,0) in the slope of the curve, we get

Therefore the slope of the normal to the curve at (0,0) is -1

Hence the equation of the normal to the curve y=tanx at (0,0) is

y-0=-1(x-0)

⇒ y=-x

or x+y=0