Question

Найти 1+5cos2α, если tgα=−3

Answer 1

Решение задания смотри на фотографии

Answer 2

To find the value of 1 + 5cos(2α) when tg(α) = -3, we need to first determine the value of cos(2α).

We know that: tan(α) = -3

We can use the identity for tan(2α) in terms of tan(α): tan(2α) = (2 * tan(α)) / (1 - tan^2(α))

Let's plug in the given value: tan(2α) = (2 * (-3)) / (1 - (-3)^2) tan(2α) = (-6) / (1 - 9) tan(2α) = (-6) / (-8) tan(2α) = 3/4

Now, we can use the identity for cos(2α) in terms of tan(2α): cos(2α) = (1 - tan^2(2α)) / (1 + tan^2(2α))

Let's calculate the value of cos(2α): cos(2α) = (1 - (3/4)^2) / (1 + (3/4)^2) cos(2α) = (1 - 9/16) / (1 + 9/16) cos(2α) = (16/16 - 9/16) / (16/16 + 9/16) cos(2α) = (7/16) / (25/16) cos(2α) = 7/25

Now, we can find 1 + 5cos(2α): 1 + 5cos(2α) = 1 + 5 * (7/25) 1 + 5cos(2α) = 1 + 35/25 1 + 5cos(2α) = 1 + 7/5 1 + 5cos(2α) = (5 + 7) / 5 1 + 5cos(2α) = 12 / 5

So, when tg(α) = -3, 1 + 5cos(2α) is equal to 12/5 or 2.4.