We have the functions
#x=t-sint# and #y=1-cost#
If we find out #dy/dt# and #dx/dt# we can divide them and find #dy/dx#
#(dy/dt)/(dx/dt)# #-># #(dy/canceldt)/(dx/canceldt)# #-># #dy/dx#
#color(red)1.# #y=1-cost#
Differentiate both sides with respect to #t#
#d/dty=d/dt(1-cost)#
#dy/dt=0-(-sint)#
#dy/dt=sint# #-># #color(red)A#
#color(red)2.# #x=t-sint#
Differentiate both sides with respect to #t#
#d/dtx=d/dt(t-sint)#
#dx/dt=1-cost# #-># #color(red)B#
Now we divide #color(red)A# and #color(red)B#
#(dy/dt)/(dx/dt)=sint/(1-cost)#
#dy/dx=sint/(1-cost)#
