task/29820090 решить уравнение sinx*cosx*cos2x*cos8x =(1/4)*sin12x
решение sinx*cosx*cos2x*cos8x =(1/4)*sin12x ⇔ sin4x*cos8x = sin12x ;
* * * sinα*cosα =(1/2)*sin2α * * * ⇔ sin4x*cos8x = sin(4x+8x) ⇔
sin4x*cos8x = sin4x*cos8x + cos4x*sin8x ⇔ cos4x*sin8x =0 ⇔
sin8x =0 ⇒ 8x = π*k , k ∈ℤ ; x = (π/8)*k , k ∈ℤ
ответ : (π/8)*k , k ∈ ℤ .