Дано уравнение |cosx| = -sqrt3 * sinx

Question

Дано уравнение |cosx| = -sqrt3 * sinx

Answer 1

1)сosx<0<br>x∈(π/2+2πn;3π/2+2πn,n∈z)
-cosx=-√3sinx
cosx-√3sinx=0
2(1/2cosx-√3/2sinx)=0
2cos(x+π/3)=0
x+π/3=π/2+πn,n∈z
x=π/6+πn,n∈z
нет решения
2)сosx≥0
x∈[-π/2+2πn;π/2+2πn,n∈z]
cosx=-√3sinx
cos(x-π/3)=0
x-π/3=π/2+πn
x=5π/6+πn,n∈z