$\text{ If }x=a(t-sint),y=a(1-cost)\text{ if }\frac{dy}{dx}=\cot p\text{ then }p=$

$\begin{array}{l}x=a(t-\sin t)\Rightarrow \frac{dx}{dt}=a(1-\cos t)\\ y=a(1-\cos t)\Rightarrow \frac{dy}{dt}=a\sin t\end{array}$

$\begin{array}{l}\frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}\\ =\frac{a\sin t}{a(1-\cos t)}\\ =\frac{2\sin \frac{t}{2}\cos \frac{t}{2}}{2{\sin }^2\frac{t}{2}}\\ \frac{dy}{dx}=\cot \frac{t}{2}\\ \therefore p=\frac{t}{2}\end{array}$