Question

2cos²x –senx -1 =0 no intervalo 0 ≤x ≤2 π

Answer 1

2cos² x - sen x - 1 = 0
2(1 - sen² x) - sen x - 1 = 0
2 - 2sen² x - sen x - 1 = 0
- 2sen² x - sen x + 1 = 0
  2sen² x + sen x - 1 = 0

sen x' = 1/2

sen x" = - 1


sen x = - 1/2

x = a + 2kπ
x = π - π/6 + 2kπ
x = 5π/6 + 2kπ

x = a + 2kπ
x = 2π - π/6 + 2kπ
x = 11π/6 + 2kπ

S = {5π/6, 11π/6}