1. Sin 3x = - cos x

2. Sin x + cos x = 1/sin x + 1/cos x

3. Sin 2x - √3 cos2x = 2 sin 5x

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 2 х - Sin π/3Cos 2x = Sin 5x

Sin (2x - π/3) - Sin 5x = 0

2Sin (x - π/6 + 2,5 х) 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