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When you differentiate first time i.e. we get
dy/dx=sint/1-cost
Now convert this expression into simple form using trignometric identities
dy/dx=2(sint/2 cost/2)/2sin^2t/2
We get dy/dx = cot(t/2)
Now again differentiating with reference to dx
We get -cosec^2(t/2) dt/dx
Now
d²y/dx²= -cosec^2(t/2) dt/dx
=-cosec^2(t/2)/dx/dt
From question
dx/dt=a(1-cost)
So at last
d²y/dx²==-cosec^2(t/2)/a(1-cost)
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