`sinxtanx-1=tanx-sinx`

Explanation

`sinx. Tanx = tanx-sinx+1`
`rArr sinx. Tanx-tanx+sinx-1=0`
`rArr tan x(sinx-1)+1(sinx-1)=0`
`rArr (sinx-1)(tanx+1)=0`
`rArr sin x-1=0 or tan x+1=0`
`rArr sin x= 1 " or "tanx=-1`
`rArr sin x=sin.(pi)/(2)" or "tanx=-tan.(pi)/(4)`
`rArr sin x=sin.(pi)/(2)" or "tanx=tan(pi-(pi)/(4))`
`rArr sin x=sin.(pi)/(2)" or "tanx=tan.(3pi)/(4)`
`therefore" "alpha_(1)=(pi)/(2)" or "alpha_(2)=(3pi)/(4)`
`therefore" "` The general solution are
`theta = npi +(-1)^(n).(pi)/(2)`