Question

Решите неравенство:
$1-2sin4x textless cos^{2} 4x$

Answer 1

1-2sin4x<1-sin²4x
sin²4x-2sin4x<0
sin4x(sin4x-2)<0
1
{sin4x<0⇒π+2πk<4x<2π+2πk⇒π/4+πk/2<x<π/2+πk/2
{sin4x>2 нет решения
2
sin4x>0⇒2πk<4x<π+2πk⇒πk/2<x<π/4+πk/2
{sin4x<2⇒x∈R
x∈(πk/2;π/4+πk/2,k∈z)