x=-π/4+πn
x=(-1)^n•π/12+(π/2)•n
Объяснение:
cos4x-sin2x=0
cos²2x-sin²2x-sin2x=0
1-2sin²2x-sin2x=0
2sin²2x+sin2x-1=0
sin2x=(-1±3)/4
1) sin2x=-1 => 2x=-π/2+2πn => x=-π/4+πn
2) sin2x=½ => 2x=(-1)^n•π/6+πn => x=(-1)^n•π/12+(π/2)•n
x=-π/4+πn
x=(-1)^n•π/12+(π/2)•n
Объяснение:
cos4x-sin2x=0
cos²2x-sin²2x-sin2x=0
1-2sin²2x-sin2x=0
2sin²2x+sin2x-1=0
sin2x=(-1±3)/4
1) sin2x=-1 => 2x=-π/2+2πn => x=-π/4+πn
2) sin2x=½ => 2x=(-1)^n•π/6+πn => x=(-1)^n•π/12+(π/2)•n