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