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Question

At any point t on the curve x=a(t+sint),y=a(1cot), find the length of the tangent, normal subtangent and subnormal .

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Solution

x=a(t+sint)dxdt=a.cost
y=a(1cot)=dydt=a.sint
dydx=tant
length of tangent
y11+f(x1)2f(x1)
=a(1cost)(1+tan2t)tant
length of sub normal
=y1f(x1)
=a(1cost)tant

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