Question

Алгебра, 10 класс
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Answer 1

$1)\frac{Cos(\pi-\beta)-3Sin(-\frac{3\pi }{2}+\beta)}{Cos(\beta-3\pi)}=\frac{Cos(\pi-\beta)+3Sin(\frac{3\pi }{2}-\beta)}{Cos(\pi- \beta)}=\frac{-Cos\beta-3Cos\beta}{-Cos\beta }=\\\\=\frac{-4Cos\beta }{-Cos\beta }=\boxed4\\\\\\2)\frac{Cos^{2}(\frac{3\pi }{2}+\alpha)}{tg^{2}(\alpha -2\pi)}+\frac{Cos^{2}(\pi-\alpha) }{tg^{2}(\alpha-\frac{3\pi }{2})}=\frac{Sin^{2}\alpha}{tg^{2}\alpha} +\frac{Cos^{2}\alpha}{Ctg^{2}\alpha}=$

$=\frac{Sin^{2}\alpha}{\frac{Sin^{2}\alpha}{Cos^{2}\alpha }}+\frac{Cos^{2}\alpha}{\frac{Cos^{2}\alpha}{Sin^{2}\alpha}}=\frac{Sin^{2}\alpha\cdot Cos^{2}\alpha }{Sin^{2}\alpha} +\frac{Cos^{2}\alpha\cdot Sin^{2}\alpha}{Cos^{2}\alpha}=Cos^{2} \alpha+Sin^{2}\alpha=\boxed1$