Question

Jika tan2 x − 2tan x − 8 = 0 dan 0 derajat ≤ x ≤ 1800 , maka cos x = ⋯.

Answer 1

Answer:

Step-by-step explanation:

Let tan x = u;

Then, the given equation reduces to,

u^2 - 2u - 8 = 0

or, u^2 - 4u + 2u - 8 = 0

or, u(u - 4) + 2(u - 4) = 0

or, (u - 4)(u + 2) = 0

or, u = -2, +4

or, tan x = -2, +4

Now, sec^2 x = tan^2 x + 1

= (-2)^2 + 1, 4^2 + 1

= 5, 17

or, sec x = sqrt(5), sqrt(17)

or, cos x = 1/sqrt(5), 1/sqrt(17)