1. 3 cos 2x - 5 cos x = 1

2. cos 3x - cos 5x = sin 4x

3. 2 sin x - cos x = 0

4. 3 sin^2x + sin x cos x - 4cos ^2x = 0

1.

3cos2x-5cosx=1

3 (cos²x-sin²x) - 5cosx-1=0

3cos²x-3sin²x-5cosx-1=0

3cos²x-3 (1-cos²x) - 5cosx-1=0

3cos²x-3+3cos²x-5cosx-1=0

6cos²x-5cosx-4=0

cosx=t; |t|≤1

6t²-5t-4=0

D=25-4*6 * (-4) = 25+96=121

t1 = (5+11) / 12=16/12 (не удовл. усл |t|≤1)

t2 = (5-11) / 12=-6/12=-1/2

cosx=-1/2

x=+-2 π/3+2πn; n∈z

Ответ:+-2 π/3+2πn; n∈z