Find the differentiation of `y=tan^(-1)((acosx-bsinx)/(bcosx+asinx))`

Explanation

Let `y=tan^(-1)((acosx-bsinx)/(bcosx+asinx))`
`=tan^(-1)[(((acosx)/(bcosx))-((bsinx)/(bcosx)))/(((bcosx)/(bcosx))+((asinx)/(bcosx)))]`
`=tan^(-1)[(((a)/(b))-tanx)/(1+((a)/(b))tanx)]`
`=tan^(-1)((a)/(b))-tan^(-1)(tanx)" "=tan^(-1)((a)/(b))-x`
`therefore (dy)/(dx)=(d)/(dx)[tan^(-1)((a)/(b))]-(d)/(dx)(x)=0-1`
`=-1`