1.
cosα= -1/2
α=(+/-) (2π/3) + 2πn, n∈Z
2.
2sinx-√2=0
sinx=√2/2
x=(-1)ⁿ (π/4) + πn, n∈Z
3.
2cosx+√3=0
cosx= - √3/2
x=(+/-) (5π/6) + 2πn, n∈Z
4.
2sin2x+1=0
sin2x= - 1/2
2x=(-1)ⁿ⁺¹ (π/6) + πn, n∈Z
5.
2cos(x - π/6) -√2=0
cos(x-π/6)=√2/2
x-π/6=(+/-) (π/4) + 2πn, n∈Z
x=(+/-) (π/4) + (π/6) + 2πn, n∈Z
6.
2sin(x/2 - π/3) - √3=0
sin(x/2 - π/3) = √3/2
x/2 - π/3 = (-1)ⁿ (π/3) + πn
x/2 = (-1)ⁿ (π/3) + (π/3) + πn
x=(-1)ⁿ (2π/3) + (2π/3) + 2πn, n∈Z