решить уравнение sin(4x)+cos(4x)=0

ответ:sin4x+sin(π/2-4x)=0

sin4x+sin(π/2-4x)=02sinπ/4cos(4x-π/4)=0

sin4x+sin(π/2-4x)=02sinπ/4cos(4x-π/4)=0cos(4x-π/4)=0

sin4x+sin(π/2-4x)=02sinπ/4cos(4x-π/4)=0cos(4x-π/4)=04x-π/4=π/2+πn

sin4x+sin(π/2-4x)=02sinπ/4cos(4x-π/4)=0cos(4x-π/4)=04x-π/4=π/2+πn4x=π/4+π/2+πn=3π/4+πn

sin4x+sin(π/2-4x)=02sinπ/4cos(4x-π/4)=0cos(4x-π/4)=04x-π/4=π/2+πn4x=π/4+π/2+πn=3π/4+πnx=3π/16+πn/4