[tex]\displaystyle\bf\\7)\\\\Sin\alpha Cos\beta +Cos\alpha Sin\beta =Sin(\alpha +\beta ) \\\\2Sin\alpha Cos\alpha =Sin2\alpha \\\\Sin^{2}\alpha +Cos^{2}\alpha =1\\\\1-2Sin^{2} \alpha =Cos2\alpha \\\\\\8)\\\\570^\circ=570\cdot\frac{\pi }{180} =\frac{19\pi }{6} \\\\\\280^\circ=280\cdot\frac{\pi }{180} =\frac{14\pi }{9} \\\\\\300^\circ=300\cdot\frac{\pi }{180} =\frac{5\pi }{3} \\\\\\420^\circ=420\cdot\frac{\pi }{180} =\frac{7\pi }{3}[/tex]
[tex]\displaystyle\bf\\9)\\\\Sin\alpha =\frac{3}{5} \ \ , \ \ \frac{\pi }{2} < \alpha < \pi \\\\\\Cos2\alpha =1-2Sin^{2} \alpha =1-2\cdot\Big(\frac{3}{5} \Big)^{2} =1-2\cdot\frac{9}{25} =1-\frac{18}{25} =\\\\\\=\frac{7}{25} =0,28\\\\\\Otvet: \ Cos2\alpha =0,28[/tex]
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[tex]\displaystyle\bf\\7)\\\\Sin\alpha Cos\beta +Cos\alpha Sin\beta =Sin(\alpha +\beta ) \\\\2Sin\alpha Cos\alpha =Sin2\alpha \\\\Sin^{2}\alpha +Cos^{2}\alpha =1\\\\1-2Sin^{2} \alpha =Cos2\alpha \\\\\\8)\\\\570^\circ=570\cdot\frac{\pi }{180} =\frac{19\pi }{6} \\\\\\280^\circ=280\cdot\frac{\pi }{180} =\frac{14\pi }{9} \\\\\\300^\circ=300\cdot\frac{\pi }{180} =\frac{5\pi }{3} \\\\\\420^\circ=420\cdot\frac{\pi }{180} =\frac{7\pi }{3}[/tex]
[tex]\displaystyle\bf\\9)\\\\Sin\alpha =\frac{3}{5} \ \ , \ \ \frac{\pi }{2} < \alpha < \pi \\\\\\Cos2\alpha =1-2Sin^{2} \alpha =1-2\cdot\Big(\frac{3}{5} \Big)^{2} =1-2\cdot\frac{9}{25} =1-\frac{18}{25} =\\\\\\=\frac{7}{25} =0,28\\\\\\Otvet: \ Cos2\alpha =0,28[/tex]