If x=theta-sinthetaandy=1-costheta,"find...

If `x=theta-sinthetaandy=1-costheta,"find"(dy)/(dx)" at "theta=(pi)/(2)`

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`x=theta-sinthetaandy=1-costheta`,
Differentiating x and y w.r.t., `theta`, we get,
`(dx)/(d theta)=(d)/(d theta)(theta-sintheta)=1-costheta`
`and (dy)/(d theta)=(d)/(d theta)(1-costheta)=0-(-sintheta)=sintheta`
`therefore(dy)/(dx)=(dy//d theta)/(dx//d theta)=(sintheta)/(1-costheta)`
`=(2sin(theta//2)cos(theta//2))/(2sin^(2)(theta//2))=cot((theta)/(2))`
`therefore((dy)/(dx))_(at theta=pi//2)=cot.(pi)/(4)=1`

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