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if x= a(t+sint) ;y=a(1-cost) then y2 that is second order derivative

if x= a(t+sint) ;y=a(1-cost) then y2 that is second order derivative
 

Grade:12

1 Answers

Arun
25763 Points
2 years ago

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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