Question

решите уравнение :
sin7x-cos13x=0

Answer 1

sin7x-cos13x=0
Cos(π/2 - 7x) - Cos13x = 0
-2Sin(π/4 -2x)Sin(π/4 -10x) = 0
Sin(π/4 -2x)  = 0   или   Sin(π/4 -10x) = 0
π/4 -2x = nπ, n ∈Z            π/4 -10x = πk , k ∈ Z
2x = π/4  - nπ, n ∈Z          10x = π/4 - πk , k ∈Z
x = π/8 - nπ/2 , n ∈Z            x = π/40 - πk/10 , k ∈Z