Question

Вычислите tg 4 альфа, если тангенс альфа равен 1\8

Answer 1

$tg2a = \frac{2tga}{1-tg^2a}$

$tg2a = \frac{2*\frac{1}{8}}{1-\frac{1}{64}} = \frac{1}{4}:\frac{63}{64} = \frac{64}{4*63} = \frac{16}{63}$ 

$tg4a = \frac{2tg2a}{1-tg^22a}$ 

$tg4a = \frac{2*\frac{16}{63}}{1-\frac{16^2}{63^3}} = \frac{32}{63}:\frac{3969-256}{3969} = \frac{32*3969}{63*3713}=\frac{32*63}{3713}=\frac{2016}{3713}$