Find an equation in x and y for the line tangent to the curv

Find an equation in x and y for the line tangent to the curve at t= pi/3.

Can you please show work when derving the answer?

Solution

dx/dt= 3cos^2(4t)*4
at t=pi/3
dx/dt= 3
dy/dt= 3sin^2(10t)*10
at t=pi/3
dy/dt= 45/4
dy/dx=45/12
=15/4
(y-33/8)=15/4(x-1/8)

4y-33/2=15x-15/8