1) sin^2 x = 1
sin x = -1, x1 = -pi/2 + 2pi*k
sin x = 1, x2 = pi/2 + 2pi*k
3) cos^2 x = cos x
cos^2 x - cos x = 0
cos x*(cos x - 1) = 0
cos x = 0, x = pi/2 + pi*k
cos x = 1, x = 2pi*k
5) tg x = 3ctg x
tg x = 3*1/tg x
tg^2 x = 3
tg x = -√3, x1 = -pi/3 + pi*k
tg x = √3, x2 = pi/3 + pi*k
7) 2sin^2 x + cos^2 x - 3sin x - 5 = 0
sin^2 x + sin^2 x + cos^2 x - 3sin x - 5 = 0
sin^2 x + 1 - 3sin x - 5 = 0
sin^2 x - 3sin x - 4 = 0
(sin x - 4)(sin x + 1) = 0
sin x = 4 - решений нет
sin x = -1, x = -pi/2 + 2pi*k
8) 2sin^2 x + 3cos x = 0
2 - 2cos^2 x + 3cos x = 0
2cos^2 x - 3cos x - 2 = 0
(cos x - 2)(2cos x + 1) = 0
cos x = 2 - решений нет
cos x = -1/2
x1 = 2pi/3 + 2pi*k
x2 = 4pi/3 + 2pi*k