ask about coordinate question

(a)
dy/dt=4sintcost
dx/dt=-2csc^2t
dy/dx=(dy/dt)/(dx/dt)=(4sintcost)/(-2csc^2t)=-2sin^3tcost
sub t=45'
dy/dx=-2*(4/16)=-1/2
when t=45
x=2,y=2(1/2)=1
equation of tangent to curve at point where t=45'
y-1=-1/2(x-2)
2y-2=-x+2
x+2y-4=0
(b)
x=2cot t, y= 2sin^2 t
csc^2t=2/y
using 1+cot^2t=csc^2t
1+(x/2)^2=2/y
4+x^2=8/y
y(4+x^2)=8
y=8/(4+x^2)
The curve is defined for all values of t except nπ or (n+1/2)π or (n-1/2)π where n is an integer