Question

Tg a = 4 tg2a=? ..............

Answer 1

Ответ:

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

Объяснение:

$tg\alpha=4$

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

$sin\alpha=4cos\alpha$

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

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

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

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

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

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

Answer 2

To find the value of tg(2a), given that tg(a) = 4, we can use the double-angle identity for the tangent function.

The double-angle identity for tangent states that:

tg(2a) = (2 * tg(a)) / (1 - tg^2(a))

Let's substitute the given value of tg(a) = 4 into the equation:

tg(2a) = (2 * 4) / (1 - 4^2)

tg(2a) = 8 / (1 - 16)

tg(2a) = 8 / (-15)

Therefore, tg(2a) is equal to -8/15.