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

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