Решите уравнение: cos⁡3 х + cos⁡2 х = sin⁡5 х

2 сos (5x/2) cos (x/2) - 2sin (5x/2) cos (5x/2) = 0

2cos (5x/2) * (cos (x/2) - sin (5x/2)) = 0

cos (5x/2) = 0⇒5x/2=π/2+πn⇒x=π/5+2πn/5, n∈z

cos (x/2) - sin (5x/2) = 0

cos (x/2) - cos (π/2-5x/2) = 0

-2sin (3x/2-π/4) sin (-x+π/4) = 0

2sin (3x/2-π/4) sin (x-π/4) = 0

sin (3x/2-π/4) = 0⇒3x/2-π/4=πk⇒3x/2=π/4+πk⇒x=π/6+2πk/3, k∈z

sin (x-π/4) = 0⇒x-π/4=πm⇒x=π/4+πm, m∈z