Given $x = sin^2(t)$, $y = cos^2(t)$, I need to find $\frac{dy}{dx}$ in every non-singular point of the curve.
So $\frac{dy}{dt} = -2sin(t)cos(t)$ and $\frac{dx}{dt} = sin(2t)$.
To find the singularity points -
$\frac{dy}{dt} = \frac{dx}{dt} = 0\iff sin(2t)=sin(t)=0 \iff t=k\pi$
So for every $t \not=k\pi$, $\frac{dy}{dx}=\frac{-2sin(t)cos(t)}{sin(2t)}=\frac{-sin(2t)}{sin(2t)}=-1$
Am I correct so far? is it true that the linear equation for this curve is $y=1-x$?
Thanks