Question

$cos(-2 \alpha)+2sin( \pi -2 \alpha )/ctg \alpha +ctg( \pi /2+ \alpha ).$ . De dus la o forma mai simpla. AJUTOR AM TEZA MINEE ^o^ !!!!!!!!!!!!!

Answer 1

Functia cos este para si in consecinta cos(-2α)=cos2α.
sin(π-2α)=sinπ·cos2α-sin2α·cosπ=-sin2α·(-1)=sin2α
2sin(π-2α)/(sinα/cosα)=2sin2α·cosα/sinα=2·2sinαcosα·cosα/sinα=4cos²α
ctg(π/2+α)=sin(π/2+α)/cos(π/2+α)=
=[sinπ/2·cosα+sinα·cosπ/2]/[cosπ/2·cosα-sinπ/2·sinα]=
=cosα/(-sinα)=-ctgα
Relatia intiala=cos2α+4cos²α-ctgα