1. Упростить: (cos2x-sin2x-2cos^ (2) x) / (cosx+sinx)

2. Доказать тождество: (sin2x-sinx) / (1-cosx+cosx) = tgx

1. Расписываем sin2x=2sinx*cosx и cos2x=cos²x-sin²x. Получается:

(cos²x-sin²x-2sinx*cosx - 2cos²x) / (cosx+sinx) = - (cos²x+2sinx*cosx+sin²x) / (cosx+sinx) = - (cosx+sinx) ² / (cosx+sinx) = - cosx-sinx

2. (sin2x-sinx) / (1-cosx+cos2x) = (2sinx*cosx-sinx) / (1-cosx+cos²x-sin²x) =

= sinx (2cosx-1) / (sin²x+cos²x - cosx+cos²x-sin²x) =

= sinx (2cosx-1) / (2cos²x-cosx) =

= sinx (2cosx-1) / cosx (2cosx-1) = sinx/cosx = tgx