Question

Вычислите tgB, если...

Answer 1

$\displaystyle\bf\\\frac{Cos(\alpha +\beta )}{Cos(\alpha -\beta )} =\frac{2}{3} \\\\3Cos(\alpha +\beta )=2Cos(\alpha -\beta )\\\\3(Cos\alpha Cos\beta -Sin\alpha Sin\beta )=2(Cos\alpha Cos\beta +Sin\alpha Sin\beta)\\\\3Cos\alpha Cos\beta -3Sin\alpha Sin\beta =2Cos\alpha Cos\beta +2Sin\alpha Sin\beta=0\\\\Cos\alpha Cos\beta =5Sin\alpha Sin\beta \ |:Sin\alpha Sin\beta\neq 0 \\\\\\\frac{Cos\alpha Cos\beta }{Sin\alpha Sin\beta }=\frac{5Sin\alpha Sin\beta }{Sin\alpha Sin\beta }$

$\displaystyle\bf\\Ctg\alpha \cdot \underbrace{Ctg\beta }_{5}=5\\\\Ctg\beta \cdot 5=5\\\\Ctg\beta =1\\\\tg\beta =\frac{1}{Ctg\beta } =\frac{1}{1} =1\\\\\\Otvet:tg\beta =1$