Автор - Дмитрий Кеглев

Cos(2x-pi/5)=-√2/2. sin(2x+π/7)=1/2. sin6x+cosx+sin4x=0. Решить уравнения

Ответ

Автор - aksioma)
sin6x+cosx+sin4x=0,

2sin5xcosx+cosx=0,

cosx(2sin5x+1)=0,

1)cosx=0, x= Pi/2 +pin,n€Z

2)sin5x=-1/2,

5x =(-1)^k Pi/6 + Pik, k€Z,

x= (-1)^k Pi/30 + Pik/5, k€Z;

Cos(2x-pi/5)=-√2/2

(2x-pi/5)=±3Pi/4 +2Pin,n€Z

2x= ±3Pi/4 +pi/5+2Pin,n€Z

x=±3Pi/8 +pi/10+Pin,n€Z

х1=19pi/40+Pin,n€Z
x2= - 11pi/40 +Pin,n€Z

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