5.
tgx=1/ctgx, ctgx=1/tgx
(tgx+ctgx)/(1+ctg^2 x)=tg^2 x*(tgx+1/tgx)/(tg^2x+1)=tg^2 x*1/tgx*(tg^2 x+1)/(tg^2 x+1)=tgx*1=tgx
6.
tgx=sinx/cox, sin^2 x+ cos^ x=1
1/(cos^2 x-sin^2 x)=(1+tg^2 x)/(1-tg^2 x)=(1+sin^2 x/cos^2 x)(1-sin^2 x/cos^2 x)= ((cos^2 x+sin^2 x)/cos^2 x)/(cos^2 x -sin^2 x )/cos^2 x
(1/cos^2 x)*(cos^2 x/(cos^2 x- sin^2 x)=1/(cos^2 x- sin^2 x)
7.
tgx*ctg x=1
(sinx+tg x)(cosx+ctgx)=(1+sinx)(1+cosx)
sinx*cosx+sinx*cosx/sinx+sinx/cosx*cosx+ tgx*ctgx)=1+sinx+cosx+sinx*cosx
sinx*cosx+cosx+sinx+1=1+sinx+cosx+sinx*cosx
