2sin(x+π/6)≤√3
sin(x+π/6)≤√3/2
5π/6+2πn≤x+π/6≤13π/6+2πn
5π/6-π/6+2πn≤x≤13π/6-π/6+2πn
2π/3+2πn≤2π+2πn,n∈z
x∈[2π/3+2πn;2π+2πn,n∈z]
2cos(x-π/3)>-√2
cos(x-π/3)>-√2/2
-3π/4+2πn-3π/4+π/3+2πn-5π/12+2πnx∈(-5π/12+2πn;13π/12+2πn,n∈z)
2sin²x+5cosx-4=0
2-2cos²x+5cosx-4=0
cosx=a
2a²-5a+2=0
D=25-16=9
a1=(5-3)/4=1/2⇒cosx=1/2⇒x=+-π/3+2πn,n∈z
a2=(5+3)/4=2⇒cosx=2>1 нет решения