Cos2x + 5sin| x | = 3 решите уравнение

Cos2x + 5sin| x | = 3 решите уравнение

1) x>0

Cos2x + 5sin| x | = 3 Cos2x + 5sin x = 3 1-2sin² x + 5sin x = 3

-2sin² x+5sin x-2 = 0 2sin² x-5sin x+2 = 0

sin x=t 2t² - 5t+2 = 0 t1=[5-√ (25-16) ]/4 = (5-3) / 4 = 1/2

t2=[5+√ (25-16) ]/4 = 2

sin x=1/2 x = (-1) ⁿ (π/6) + πn, n∈Z

sin x=2 нет решений

2) 1) x<0

Cos2x + 5sin| x | = 3 Cos2x - 5sin x = 3 1-2sin² x - 5sin x = 3

-2sin² x-5sin x-2 = 0 2sin² x+5sin x+2 = 0

sin x=t 2t² + 5t+2 = 0 t1=[-5-√ (25-16) ]/4 = (-5-3) / 4 = - 2

t2=[-5+√ (25-16) ]/4 = (-5+3) / 4=-1/2

sin x=-1/2 x = (-1) ^ (n+1) (π/6) + πn, n∈Z

sin x=-2 нет решений

ответ

x = (-1) ⁿ (π/6) + πn, n∈Z

x = (-1) ^ (n+1) (π/6) + πn, n∈Z