Question

N.8.054 помогите решить пожалуйста

Answer 1

sinx+sin7x-cos5x+cos3x=0
(sinx+sin7x)+(cos3x-cos5x)=0
2sin4xcos3x+2sin4xsinx=0
2sin4x*(cos3x+sinx)=0
sin4x=0⇒4x=πk⇒x=πk/4,k∈z
cos3x+sinx=0
cos3x+cos(π/2-x)=0
2cos(x+π/4)*cos(2x-π/4)=0
cos(x+π/4)=0⇒x+π/4=π/2+πk⇒x=π/4+πk,k∈z
cos(2x-π/4)=0⇒2x-π/4=π/2+πk⇒2x=3π/4+πk⇒x=3π/8+πk/2,k∈z