Решите уравнения. 1) sin3x*cosx=1+sinx*co3x 2) sinx*cosx=0
1) sin 3x*cos x - cos 3x*sin x = 1
sin (3x - x) = sin 2x = 1
2x = π/2 + 2π*k; k ∈ Z
x = π/4 + π*k; k ∈ Z
2) sin x*cos x = 0
1/2*2sin x*cos x = 1/2*sin 2x = 0
sin 2x = 0
2x = π*k, k ∈ Z
x = π/2*k, k ∈ Z