Question

Знайдіть tg2a якщо tga=-2

Answer 1

$tg2\alpha =\frac{2tg\alpha }{1-tg^2\alpha }=\frac{2*(-2)}{1-(-2)^2}=\frac{-4}{1-4}=\frac{4}{3}$

Answer 2

To find the value of tg(2a) given that tga = -2, we need to use the trigonometric identity:

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

Given that tga = -2, we can substitute this value into the identity:

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

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

tg(2a) = (-4) / (-3)

Now, we can simplify by dividing both the numerator and denominator by the greatest common divisor (GCD), which is 1 in this case:

tg(2a) = 4/3

So, the value of tg(2a) is 4/3.