1)1-ctg^2(x)=(1+ctg^2(x))(sin^2(x)-cos^2(x))
1+ctg^2(x)=1/sin^2(x)
1/sin^2(x)(sin^2(x)-cos^2(x))
(1/sin^2(x)(sin^2(x))-1/sin^2(x)cos^2(x)=1-cos^2(x)/sin^2(x)=1-ctg^2(x)
2)1-sin^2(x)+ctg^2(x)*sin^2(x)=cos^2(x)+cos^2(x)/sin^2(x)*sin^2(x)=2cos^2(x);
3) (tgxcosx)^2+(ctgxsinx)^2=tg^2(x)cos^2(x)+ctg^2(x)*sin^2(x)=sin^2(x)/cos^2x * cos^2(x)+cos^2(x)/sin^2(x) * sin^2(x)=sin^2(x)+cos^2(x)=1.
1+ctg^2(x)=1/sin^2(x)
1/sin^2(x)(sin^2(x)-cos^2(x))
(1/sin^2(x)(sin^2(x))-1/sin^2(x)cos^2(x)=1-cos^2(x)/sin^2(x)=1-ctg^2(x)
2)1-sin^2(x)+ctg^2(x)*sin^2(x)=cos^2(x)+cos^2(x)/sin^2(x)*sin^2(x)=2cos^2(x);
3) (tgxcosx)^2+(ctgxsinx)^2=tg^2(x)cos^2(x)+ctg^2(x)*sin^2(x)=sin^2(x)/cos^2x * cos^2(x)+cos^2(x)/sin^2(x) * sin^2(x)=sin^2(x)+cos^2(x)=1.