Объяснение:

1.

[tex]a)\ 160^0=\frac{160^0*\pi }{180^0} =\frac{8\pi }{9}.\\ b)\ \frac{5\pi }{9}=\frac{5\pi *180^0}{9*\pi } = 5*20^0=100^0.\\[/tex]

2.

[tex]\frac{sin\alpha }{1+cos\alpha }+ctg\alpha =\frac{sin\alpha }{1+cos\alpha } +\frac{cos\alpha }{sin\alpha } =\frac{sin\alpha*sin\alpha +(1+cos\alpha )*cos\alpha }{(1+cos\alpha)*sin\alpha } =\frac{sin^2\alpha +cos\alpha +cos^2\alpha }{(1+cos\alpha )*sin\alpha } =[/tex]

[tex]=\frac{1+cos\alpha }{(1+cos\alpha )*sin\alpha } =\frac{1}{sin\alpha } =cosec(\alpha ).[/tex]