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If x=a(theta-sintheta) , y=a(1+costheta)...

If `x=a(theta-sintheta)` , `y=a(1+costheta)` find `(d^2y)/(dx^2)`

Text Solution

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`x=a (theta-"sin" theta)`
`rArr (dx)/(d theta) = a (1-"cos" theta) = 2a " sin"^(2)(theta)/(2)`
`y = a(1 + "cos" theta)`
`rArr (dy)/(d theta) = -a"sin" theta = -2a"sin" (theta)/(2) "cos" (theta)/(2)`
`therefore (dy)/(dx) = (dy//d theta)/(dx//d theta) = -(2a"sin"(theta)/(2)"cos" (theta)/(2))/(2a"sin"^(2)(theta)/(2)) = -"cot"(theta)/(2)`
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