Parametric..?

Question

A curve has parametric equations x= ln (cot x/2) - cosx and y=sinx.

Show that dy/dx= - tanx

Show ur workings plzzzz

Answer 1

The parameter should be called t
x=-ln tan t/2 -cos t as cot = 1/tan and ln(1/tan)=-ln tan
y= sin t
dy/dt =cos t
dx/dt= -1/tan(t/2)*(1+tan^2t/2)*1/2+sin t
(1+tan^2 t/2)/2 tan(t/2)=1/sin t so
dx/dt =sint -1/sin t = -cos^2t/sin t
dy/dx = dy/dt/dx/dt = -sin t/cos t =-tan t