Решите неравенствоsqrt(3)cosx-sinx<=1

Question

Решите неравенство
sqrt(3)cosx-sinx<=1

Answer 1

2(√3/2сosx-1/2sinx)≤1
2sin(π/3-x)≤1
sin(π/3-x)≤1/2
5π/6+2πn≤π/3-x≤13π*6+2πn
5π/6-π/3+2πn≤-x≤13π*6-π/3+2πn
π/2+2πn≤-x≤11π/6+2πn
-11π/6+2πn≤x≤-π/2+2πn
x∈[-11π/6+2πn;-π/2+2πn]