Question

SOLVE.. 2 cos 3x - 1 = 0

Answer 1

2cos 3x-1=0
2cos 3x=1
cos 3x=1/2
3x=cos⁻¹ 1/2     (cos⁻¹ (1/2)= π/3  + 2Kπ)   and   cos⁻¹(1/2)=5π/3+2kπ

1)
3x=π/3+2kπ
x=π/9+2/3(kπ)                   K∈Z;   K=...-2,-1,0,1,2...

2)
3x=5π/3+2kπ
x=5π/9+(2/3)kπ

Answer: 
x=π/9+2/3(kπ) U 5π/9+(2/3)kπ     ; K∈Z