Question

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

Answer 1

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