Question

tg a = 4
tg2a=?
..............

Answer 1

Ответ:

$tg2\alpha=-\frac{8}{15}$

Объяснение:

$tg\alpha=4$

$\frac{sin\alpha}{cos\alpha}=4$

$sin\alpha=4cos\alpha$

$tg2\alpha=\frac{sin2\alpha}{cos2\alpha}$

$tg2\alpha=\frac{2sin\alpha cos\alpha}{cos^2\alpha-sin^2\alpha}$

$tg2\alpha=\frac{2\cdot 4cos\alpha\cdot cos\alpha}{cos^2\alpha-(4cos\alpha)^2}$

$tg2\alpha=\frac{8cos^2\alpha}{cos^2\alpha-16cos^2\alpha}$

$tg2\alpha=\frac{8cos^2\alpha}{-15cos^2\alpha}$

$tg2\alpha=-\frac{8}{15}$