Question

Решите, пожалуйста.
Желательно с объяснениями.
cos²(3π/2+a)/tg²(a-2π)+cos²(π-a)/tg²(a-3π/2)

Answer 1

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