1. 3 cos 2x - 5 cos x = 12. cos 3x - cos 5x= sin 4x3. 2 sin x - cos x =04. 3 sin^2x + sin...

Question

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

Answer 1

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=+-2π/3+2πn; n∈z

Ответ:+-2π/3+2πn; n∈z