Question

cos5x-cosx=2sin3x
Очень нужно

Answer 1

cos5x-cosx=2sin3x
-2sin(5x+x)/2 *sin(5x-x)/2=2sin3x
-2sin3x*sin2x=2sin3x
2sin3x+2sin3x*sin2x=0
2sin3x(1+sin2x)=0|:2
sin3x=0                 1+sin2x=0
3x=Пn, n∈Z           sin2x=-1
x=Пn/3, n∈Z          2x=-П/2+2Пn,n ∈Z
                               x=-П/4+Пn, n∈Z