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<br>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