`sinxtanx-1=tanx-sinx`

Explanation

`sinxtanx=tanx-sinx+1`
`therefore sinx tan x-tanx+sinx-1=0`
`therefore tanx(sinx-1)+1(sinx-1)=0`
`therefore (sinx-1)(tanx+1)=0`
`therefore` either `sinx-1=0 or tanx+1=0`
`therefore` either `sin x=1 or tan x=-1 `
`therefore` either ` sin x=sin.(pi)/(2) or tanx=-tan.(pi)/(4)....[because sin.(pi)/(2)=1,tan.(pi)/(4)=1]`
`therefore` either `sinx=sin.(pi)/(2) or tanx=tan(pi-(pi)/(4)).....[because tan(pi-theta)=-tan theta]`
`therefore `either ` sin x=sin.(pi)/(2) or tan x=tan.(3pi)/(4)`
The general solution of `sin theta = sin alpha` is `theta= n pi +(-1)^(n)alpha, n in Z` and `tan theta = tanalpha is theta = n pi +alpha, n in Z`
`therefore` the required solution is given by `x= n pi +(-1)^(n)(pi)/(2), n in Z or x=n pi +(3pi)/(4), n in Z`.