2sin x - 4cos x - sin x/cos x - cos x/sin x + 2cos^2 x/sin x + 2 = 0
Умножаем все на sin x*cos x
2sin^2 x*cos x - 4cos^2 x*sin x - sin^2 x - cos^2 x + 2cos^3 x + 2sin x*cos x = 0
2sin x*cos x*(sin x - cos x)
- 2sin x*cos^2 x + 2cos^3 x =
= sin^2 x + cos^2 x - 2sin x*cos x
2sin x*cos x*(sin x - cos x) + 2cos^2 x*(cos x - sin x) = (sin x - cos x)^2
(sin x - cos x)*(2sin x*cos x - 2cos^2 x)
= (sin x - cos x)^2
2cos x*
(sin x - cos x)* (sin x - cos x)
= (sin x - cos x)^2
(sin x - cos x)^2*(2cos x - 1) = 0
1) sin x = cos x
tg x = 1; x1 = pi/4 + pi*k
2) cos x = 1/2
x2 = +-pi/3 + 2pi*k