Question

Решите ур-е cos4x-cosx=0 укажите корни,из промежутка [0;4П]

Answer 1

-2sin(3x/2)sin(5x/2)=0
sin(3x/2)=0
3x/2=πk
x=2πk/3
0≤2πk/3≤4π
0≤2k≤12
0≤k≤6
k=0  x=0
k=1  x=2π/3
k=2  x=4π/3
k=3  x=2π
k=4  x=8π/3
k=5  x=10π/3
k=6  x=4π
sin(5x/2)=0
5x/2=πk
x=2πk/5
0≤2πk/5≤4π
0≤2k≤20
0≤k≤10
k=0  x=0
k=1  x=2π/5
k=2  x=4π/5
k=3  x=6π/5
k=4  x=8π/5
k=5  x=2π
k=6  x=12π/5
k=7  x=14π/5
k=8  x=16π/5
k=9  x=18π/5
x=10  x=4π