Question

решить уравнение sin4x=sin2x

Answer 1

$sin4x=sin2x$

$2sin2x*cos2x=sin2x$

$2sin2x*cos2x-sin2x=0$

$sin2x(2cos2x-1)=0$

$sin2x=0 => 2x=pi n; n e Z => x=frac{pi n}2 ; ne Z$

$2cos2x-1=0=>cos2x=frac{1}2$

$2x=frac{pi}3+2pi n; n e Z=>x=frac{pi}6+pi n; n e Z;$

$2x=frac{2pi}3+2pi n; n e Z=> x=frac{2pi}6+pi n; n e Z=> x=frac{pi}3+pi n; n e Z$