Question

Решить уравнение sin4x+cos4x=0

Answer 1

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

Answer 2

$sin4x+cos4x=0 \ sin4x+sin( frac{ pi }{2} -4x)=0 \ cos(4x- frac{ pi }{4} )=0 \ 4x- frac{ pi }{4} = frac{ pi }{2} + pi n \ 4x= frac{3 pi }{4} + pi n \ x= frac{3 pi }{16} + frac{ pi n}{4}$