cos 2x - 1 = 0
4 cos² x + 4cos x - 3 = 0
3 tg( x 2 - pi 6 ) = ^ sqrt 3​

cos 2x - 1 = 0
cos2x=1
2x=2Пk
x=Пk

4 cos² x + 4cos x - 3 = 0
cosx=t |t|<=1 ОДЗ
4t^2+4t-3=0
t^2+t-3/4=0
t=(-1+-sqrt(1+3))/2=(-1+-2)/2
t1=-3/2 |t1|>1 не удовлетворяет ОДЗ
t2=1/2
cosx=1/2
x=+-П/3+2Пk

3tg(x/2-п/6)=√3
tg(x/2-П/6)=√3/3
x/2-П/6=П/6+Пk
x/2=П/3+Пk
x=2П/3+2Пk