Question

Sin6x+cos7x=0.С пояснениями пожалуйста

Answer 1

sin6x+sin(π/2-7x)=0
2sin(13x/2-π/4)cos(π/4-x/2)=0
sin(13x/2-π/4)=0
13x/2-π/4=πn,n∈Z
13x/2=π/4+πn,n∈Z
x=π/26+2πn/13,n∈Z
cos(π/4-x/2)=sin(x/2+π/4)=0
x/2+π/4=πk,k∈Z
x/2=-π/4+πk,k∈Z
x=-π/2+2πk,k∈Z