Lim (sin2x-sinx) / (tgx-tg2x) x->0

tgx-2tgx / (1-tg^2x) = (tg^3x-tgx) / (1-tg^2x) = tgx (tg^2x-1) / (1-tg^2x) = - tgx

(sin2x-sinx) / - tgx=sinx (2cosx-1) / - tgx=cosx (1-2cosx)

lim=1 (1-2) = - 1

(2 сos2x-cosx)

1/cos^2x-2/cos^2 (2x)

lim (x->0) [cos2x*cosx]^2*{2cos2x-cos} / (cos^2 (2x) - 2cos^2x) = (1*1) (2-1) / (1-2) = 1/-1=-1