Решение
sin3x - cos5x = 0
cos(π/2 - 3x) - cos5x = 0
- 2cos(π/2 - 3x + 5x)/2 * sin(π/2 - 3x - 5x)/2 = 0
1) cos(π/4 + x) = 0
π/4 + x = π/2 + πk, k ∈ Z
x = π/2 - π/4 + πk, k ∈ Z
x = π/4 + πk, k ∈ Z
2) sin(π/4 - 4x) = 0
4x - π/4 = πn, n ∈ Z
4x = π/4 + πn, n ∈ Z
x = π/16 + πn/4, n ∈ Z
x = π/16 - наименьшее положительное решение