Задача 12061 cos3x-sin2x=0...
Условие
математика
2474
Решение
★
sin((π/2)-3x)-sin2x=0
2sin(((π/2)-3x-2x))/2)*cos(((π/2)-3x+2x)/2)=0
2sin((π/4)-(5x/2))*cos((π/4)-(x/2))=0
sin((π/4)-(5x/2))=0 или cos((π/4)-(x/2))=0
-sin((5x/2)-(π/4)=0 или cos((x/2)-(π/4))=0
(5x/2)-(π/4)=πk, k∈Z или (x/2)-(π/4)=(π/2)+πn, n∈Z
5x/2=(π/4)+πk, k∈Z или (x/2)=(π/4)+(π/2)+πn, n∈Z
x=(π/10)+(2π/5)*k, k∈Z или x=(3π/2)+2πn, n∈Z
О т в е т. (π/10)+(2π/5)*k,(3π/2)+2πn, k, n∈Z