Sin5x = Cos4x
Sin5x - Cos4x=0
Sin5x - Sin(π/2 - 4х) = 0 ( Применим формулу разности синусов)
2Sin(9x/2 - π/4)Cos(x/2 + π/4) = 0
Sin(9x/2 - π/4) = 0 или Cos(x/2 + π/4) = 0
9x/2 - π/4 = πn , n ∈Z x/2 + π/4 = π/2 + πk , k ∈Z
9x/2 = πn + π/4 , n ∈Z x/2 = π/2 + πk - π/4 , k ∈Z
x = 2πn/9 + π/18, n ∈Z x/2 = π/4 + πk , k ∈Z
x = π/2 + 2πk , k ∈Z