The parametric equations of a curve are x=e^-t*cost y=e^-t*sint show that dy/dx=tan(t-pi/4)

Using product rule: f'g + fg'


Factor out 



Next, we have to use trig identities to equate this with tan(t - pi/4).
There are a lot of steps here, i think its easiest to start at either end and meet in the middle. I will show that:


Starting on left side, use angle sum identity for tan. Note tan(pi/4) = 1.


Now starting on right side:


Therefore proving that