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

-2sin (3x/2) * sin (5x/2) = 0

sin (3x/2) = 0⇒3x/2=πk⇒x=2πk/3, k∈z

0≤2πk/3≤4π

0≤k≤6

k=0 x=0

k=1 x=2π/3

k=3 x=2π

k=4 x=8π/3

k=5 x=10π/3

k=6 x=4π

sin (5x/3) = 0⇒5x/3=πk⇒x=3πk/5, k∈z

0≤3πk/5≤4

0≤k≤20/3

k=0 x=0

k=1 x=3π/5

k=2 x=6π/5

k=3 x=9π/5

k=4 x=12π/5

k=5 x=3π

k=6 x=18π/5