2) Sin x +Cos x = (Cos x + Sin x)/Sinx Cos x
Sin x Cos x(Sin x+Cos x) - Cos x + Sin x) = 0
(Cos x + Sin x)( Sin xCos x -1) = 0
а) Sin x + Cos x = 0 или б) Sin x Cos x -1 = 0
Sin x = - Cosx | : Сos x ≠0 Sin x Cos x =1
tg x = -1 0,5 Sin2x =1
x = -π/4 +πk, k∈Z Sin 2x = 2
нет решений
3) Sin 2x - √3Cos 2x = 2Sin 5x| :2
1/2Sin 2x -√3/2 Cos 2x = Sin 5x
Cos π/3 Sin 2х - Sin π/3Cos 2x = Sin 5x
Sin(2x - π/3) - Sin 5x = 0
2Sin(x - π/6 + 2,5х) Cos(x -π/6 -2,5x) = 0
a) Sin(3,5 x -π /6) = 0 или б) Cos( -1,5 x - π/6) = 0
3,5 x - π/6 = πn, где n ∈Z -1,5 x -π/6 = π/2 +πk, k∈Z
3,5 x = π/6 + πn, n∈Z -1,5 x =π/6 + π/2 +πk , k∈Z
x = π/21 + 2πn/7, n∈Z -1,5 x = 2π/3 + πk, k∈Z
x = -4π/9 - 2πk/3, k ∈Z