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Find (dy)/(dx)," if "x= a(theta+ sin the...

Find `(dy)/(dx)," if "x= a(theta+ sin theta), y= a(1- cos theta)`.

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`"We have "x=a(theta-sin theta)and y=a (1- cos theta).`
`therefore" "(dx)/("d"theta)=a(1-cos theta) and (dy)/("d"theta)=a sin theta`
`"or "(dy)/(dx)=(dy//"d" theta)/(dx//"d" theta)`
`=(a sin theta)/(a(1-cos theta))`
`=(2sin (theta//2)cos (theta//2))/(2 sin^(2) (theta//2))`
`=cot""(theta)/(2)`
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