Question

Помогите решить уравнение 2sin^x+cos5x=1

Answer 1

Сoc5x=1-2sin²x
cos5x=cos2x
cos5x-cos2x=0
2cos(3x/2)cos(7x/2)=0
cos(3x/2)=0⇒3x/2=π/2+πn,n∈z⇒x=π/3+2πn/3,n∈z
cos(7x/2)=0⇒7x/2=π/2+πk,k∈z⇒x=π/7+2πk/7,k∈z