（sin^3 x-2sin^2 x+1）/sin x-1

（sin³x-2sin²x+1）/(sin x-1)
=（sin³x-sin²x-sin²x +1）/(sin x-1)
=[（sin³x-sin²x）-（sin²x -1）]/(sin x-1)
=[ sin²x(sin x-1)- (sin x-1) (sin x+1)]/(sin x-1)
=(sin x-1)( sin²x-sinx-1) /(sin x-1)
=sin²x-sinx-1

（sin^3 x-2sin^2 x+1）/sin x-1
=（sin^3 x-sinx^4+sinx^4-2sin^2 x+1）/sin x-1
=[-sinx^3(sin x-1)+(sinx^2 -1)^2]/sin x-1
=[-sinx^3(sin x-1)+(sinx+1)^2(sinx-1)^2]/sin x-1
=(sin x-1)[(sinx+1)^2(sinx-1)-sinx^3]/sin x-1
=(sinx+1)^2(sinx-1)-sinx^3
=(sin^2x-1)(sinx+1)-sinx^3
=sinx^3+sin^2 x-sinx-1-sinx^3
=sin^2 x-sinx-1

应该是（sin^3 x-2sin^2 x+1）/(sin x-1)吧，不然这题没什么意义

=sin^2x-sinx-1

=【sin^2 x*（sin x-1）-（sin x-1）（sin x+1）】/sin x-1
=sin^2 x-sin x-1
=(sin x-1/2)^2 -5/4