Question

помогите пожалуйста ​

Answer 1

$\displaystyle\bf\\1)\\\\tg5\alpha =9\\\\tg10\alpha =\frac{2tg5\alpha }{1-tg^{2}5\alpha } =\frac{2\cdot 9}{1-9^{2} }=\frac{18}{1-81} =-0,225\\\\2)\\\\Cos\beta=\frac{1}{8} \\\\Cos2\beta =2Cos^{2}\beta -1=2\cdot\Big(\frac{1}{8} \Big)^{2} -1=2\cdot\frac{1}{64}-1=\\\\\\=\frac{1}{32}-1=0,03125-1=-0,96875 \\\\3)\\\\Cos2x=\frac{1}{9} \\\\Cos2x=1-2Sin^{2} x\\\\2Sin^{2} x=1-Cos2x=1-\frac{1}{9} =\frac{8}{9} \\\\Sin^{2} x=\frac{8}{9} :2=\frac{8}{9} \cdot\frac{1}{2} =\frac{4}{9}$

При решении были применены формулы :

$\displaystyle\bf\\\\1)\\\\tg2\alpha =\frac{2tg\alpha }{1-tg^{2}\alpha } \\\\2)\\\\Cos2\alpha =1-2Sin^{2} \alpha \\\\3)\\\\Cos2\alpha =2Cos^{2} \alpha -1$