Question

упростите выражение 26.3​

Answer 1

$1) 1 - 2Sin^{2}\alpha =\boxed{Cos2\alpha}\\\\2)2Cos^{2}\alpha-1=\boxed{Cos2\alpha}\\\\3)Ctg\alpha-tg\alpha =\frac{1}{tg\alpha }-tg\alpha=\frac{1-tg^{2}\alpha}{tg\alpha} =2*\frac{1-tg^{2} }{2tg\alpha}=\boxed{2Ctg2\alpha}\\\\4)\frac{1-tg^{2}\alpha}{1+tg^{2}\alpha}=\frac{1-\frac{Sin^{2}\alpha}{Cos^{2}\alpha} }{1+\frac{Sin^{2}\alpha}{Cos^{2}\alpha}}=\frac{(Cos^{2}\alpha-Sin^{2}\alpha)*Cos^{2}\alpha}{Cos^{2}\alpha*(Sin^{2}\alpha+Cos^{2}\alpha)}=\boxed{Cos2\alpha}$

$5)tg2\alpha(1-tg^{2}\alpha)=\frac{2tg\alpha }{1-tg^{2}\alpha} *(1-tg^{2}\alpha)=\boxed{2tg\alpha}$