1.

If x=a (t+sin t) and y=a(1-cos t ) then find `dy/dx`.

Answer» `x=a (t + sin t)`
`rArr dx/dy =a(1+cos t)`
and `y=a(1-cos t)`
`rArr dy/dx =a(0+ sin t)=a sin t `
`therefore dy/dx=(dy//dt)/(dx//dt)=(a sin t)/(a(1+cos t ))`
`=(2 sin""t/2 cos""t/2)/(2 cos^2""t/2)=tan""t/2`


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