Question

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3 tan²x - secan²x - 5 = 0, 0 ≤ x ≤ 2π

Answer 1

Verified answer

Bab Trigonometri
Matematika SMA Kelas X

3 tan² x - sec² x - 5 = 0
3 tan² x - (1 + tan² x) - 5 = 0
3 tan² x - 1 - tan² x - 5 = 0
2 tan² x - 6 = 0
2 (tan² x - 3) = 0
tan² x - 3 = 0
(tan x + √3) (tan x - √3) = 0
tan x + √3 = 0
tan x = -√3
      x = 2π/3, 5π/3

tan x - √3 = 0
tan x = √3
      x = π/3, 4π/3

HP = { π/3, 2π/3, 4π/3, 5π/3}