Question

Cos^2t - sin^2t/tg(-2)ctg2

Answer 1

sin^2(t)*cos^2(t)*[(sin^2(t)/cos^2(t))+(cos^2(t)/sin^2(t))+2)]=

=sin^2(t)*cos^2(t)*[(sin^4(t)+cos^4(t)+2cos^2(t)*sin^2(t))/sin^2(t)*cos^2(t)]=

=(cos^2(t)+sin^2(t))^2=1

Answer 2

(cost)^2-(sint)^2/tg(-2)*ctg2= (cost)^2-(sint)^2/(-1)= (cost)^2+(sint)^2=1
tg(-2)*ctg(2)=-tg(2)*ctg(2)=-1