1) cos (2x) = √2/2
2x = +-pi/4 + 2pi*k
x = +-pi/8 + pi*k
2) sin (x/3 - pi/4) = 1
x/3 - pi/4 = pi/2 + 2pi*k
x/3 = pi/2 + pi/4 + 2pi*k = 3pi/4 + 2pi*k
x = 9pi/4 + 6pi*k
2.
1 - cos x = 2sin^2 x
1 - cos x = 2 - 2cos^2 x
2cos^2 x - cos x - 1 = 0
(cos x - 1)(2cos x + 1) = 0
1) cos x = 1; x1 = 2pi*k
2) cos x = -1/2; x2 = +-2pi/3 + 2pi*k
3.
tg (3x - pi/6) = √3; Найти все корни, принадлежащие промежутку [-pi/3; pi/2]
3x - pi/6 = pi/3 + pi*k
3x = pi/3 + pi/6 + pi*k = pi/2 + pi*k
x = pi/6 + pi/3*k
x1 = pi/6 - pi/3 = -pi/6; x2 = pi/6; x3 = pi/6 + pi/3 = pi/2