3sinx + 4 sin(π/2 + x) = 4
3sinx +4 cosx = 4
6sinx/2 · cosx/2 + 4 (cos²x/2 - sin³x/2) = 4sin²x/2 + 4cos²x/2
6sinx/2 · cosx/2 - 8sin²x/2 = 0
2sin x/2 (3cosx/2 - 4sin x/2) = 0
1) 2sin x/2 = 0 → sin x/2 = 0 → x/2 = πk → x₁ = 2πk (k∈Z)
2) 3cosx/2 - 4sinx/2 = 0
делим на cosx/2 ≠ 0
4tgx2 = 3 → tgx/2 = 3/4 → x/2 = arctg 3/4 + πk → x₂ = 2arctg 3/4 + 2π (k∈Z)
Ответ: x₁ = 2πk (k∈Z); x₂ = 2arctg 3/4 + 2π (k∈Z)