Question

Уравнение: sin6x=cos4x
0<x<90

Answer 1

sin 6x = cos 4x
sin 6x - cos 4x = 0
cos (π/2 - 6x) - cos 4x = 0
-2 sin ((π/2 - 6x+ 4x)/2) * sin ((π/2 - 6x - 4x)/2) = 0
-2 sin (π/4 - x) * sin (π/4 - 5x) = 0
sin (π/4 - x) = 0   |  sin(π/4 - 5x) = 0
π/4 - x = πk         |  π/4 - 5x = πk
x = π/4 - πk         |  x = π/20 - πk/5
k ∈ Z

Ответ: x = π/4 - πk , x = π/20 - πk/5 , k ∈ Z