Question

3) sin^2a-(1+tg^2a)*cos^2a
4) sin^2a+cos^2a*(1+ctg^2a)*sin^2a

Answer 1

$3)Sin^{2}\alpha-(1+tg^{2}\alpha )*Cos^{2}\alpha=Sin^{2}\alpha-\frac{1}{Cos^{2}\alpha}*Cos^{2}\alpha=Sin^{2}\alpha-1=-Cos^{2}\alpha \\\\4)Sin^{2}\alpha+Cos^{2}\alpha*(1+Ctg^{2}\alpha)*Sin^{2}\alpha=Sin^{2}\alpha+Cos^{2}\alpha*\frac{1}{Sin^{2}\alpha}*Sin^{2}\alpha=Sin^{2}\alpha+Cos^{2}\alpha=1$