माना `y=tan^(-1)((acosx-bsinx)/(bcosx+asinx))`
`a=rsintheta,b=rcostheta`, तब `a/b=tanteta`
`rArrtheta=tan^(-1)a/b` रखने पर,
`thereforey=tan^(-1)[(r(sinthetacosx-costhetasinx))/(r(costhetacosx+sinthetasinx))]`
`rArry=tan^(-1)[(sin(theta-x))/(cos(theta-x))]`
`rArry=tan^(-1)[tan(theta-x)]`
`rArry=theta-x`
`rArry=tan^(-1)a/b-x`
दोनों पक्षों का x के सापेक्ष अवकलन करने पर,
`(dy)/(dx)=d/(dx)(tan^(-1)a/b)-d/(dx)(x)`
`[becausetan^(-1)a/b=`अचर]
`rArr(dy)/(dx)=0-1`
`(dy)/(dx)=-1`
