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Find (dy)/(dx), when x=a e^(theta)(sinth...

Find `(dy)/(dx),` when `x=a e^(theta)(sintheta-costheta),y=a e^(theta)(sintheta+costheta)`

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`x = ae^theta(sintheta-costheta)`
`:. dx/(d theta) = ae^(theta)(cos theta+sin theta)+ae^theta(sintheta-cos theta) = 2ae^thetasintheta`
`y = ae^theta(sintheta-costheta)`
`:. dy/( d theta) =ae^(theta)(cos theta-sin theta)+ae^theta(sintheta+cos theta) = 2ae^thetacostheta`
`:. dy/dx = (dy/( d theta))/(dx/( d theta)) = (2ae^thetacostheta)/(2ae^thetasintheta)`
`=> dy/dx = cot theta`.
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