Question

Найти tg2a если sina=2/5​

Answer 1

cos²α=1-sin²α=1-(2/5)²=21/25

tg²α=sin²α/cos²α=4/21

Answer 2

To find the value of tangent squared (tg^2) given the value of sine (sinα), you can use the Pythagorean identity for trigonometric functions, which states:

sin^2(α) + cos^2(α) = 1

where α is the angle in question. Then, you can use the identity:

tan^2(α) = sin^2(α) / cos^2(α)

to find the value of tangent squared.

Given that sin(α) = 2/5, we can find cos(α) using the Pythagorean identity:

sin^2(α) + cos^2(α) = 1 (2/5)^2 + cos^2(α) = 1 4/25 + cos^2(α) = 1 cos^2(α) = 1 - 4/25 cos^2(α) = 21/25

Now, we can find tan^2(α):

tan^2(α) = sin^2(α) / cos^2(α) tan^2(α) = (2/5)^2 / (21/25) tan^2(α) = (4/25) / (21/25) tan^2(α) = 4/21

So, tan^2(α) = 4/21.