N1
cos(x)^2 - sqrt(3)sin(x)cos(x) = 0
cos(x)(cos(x) - sqrt(3)sinx) = 0
cos(x) = 0 cos(x) - sqrt(3)sin(x) = 0
2(cos(x)/2 - sqrt(3)sin(x)/2) = 0
cos(x)/2 - sqrt(3)sin(x)/2 = 0
sin(π/6)cos(x) - cos(π/6)sin(x) = 0
sin(π/6 - x) = 0
x = π/2 + πn π/6 - x = πk
- x = -π/6 + πk
x = π/6 - πk
x = π/6 + πk
Ответ : x = π/2 + πn, x = π/6 + πk
N2
cos(x) =< -0,5
cos(x) = -0,5
x = -2π/3 + 2πn = 4π/3 + 2πn
x = 2π/3 + 2πn
cos(x) =< -0,5
x € [2π/3 + 2πn; 4π/3 + 2πn]
Ответ : [2π/3 + 2πn; 4π/3 + 2πn]