Упростите выражение 2(sin^2*a)-1-tga*ctga

Tg(a)=sin(a)/cos(a)
ctg(a)=1/tg(a)=cos(a)/sin(a)
sin(2a)=2*sin(a)*cos(a)
(sin(a)/cos(a)+cos(a)/sin(a))*2*sin(a)*cos(a)=(sin(a)*sin(a)/(cos(a)*sin(a))+cos(a)*cos(a)/(sin(a)*cos(a))*2*sin(a)*cos(a)=1/(sin(a)*cos(a))*(sin(a)^2+cos(a)^2)*2*sin(a)*cos(a)=в скобка получается 1=2