Question

1)2cos 2x = 1
2) 2 sin x/2 - 1 = 0

Answer 1

1. 2cosx=1
cos2x=1/2
2x=+-arccos(1/2)+2πn, n∈Z
2x=+-π/3+2πn, n∈x | :2
x=+-π/6+πn, n∈Z

2. 2sin(x/2)-1=0
2sin(x/2)=1
sin(x/2)=1/2
$frac{x}{2} =(-1) ^{n}*arcsin frac{1}{2}+ pi n,$  n∈Z

$frac{x}{2} = (-1)^{n} * frac{ pi }{6} + pi n,$n∈Z  |*2

$x= (-1)^{n} * frac{ pi }{3}+2 pi n,$n∈Z