Question

sin2x-cos2x=√3/2
Помогите пожалуйста

Answer 1

$sin2x-cos2x=frac{sqrt3}2$

Воспользуемся такой формулой: $sinx-cosx=sqrt2sin(x - frac{pi}4)$

$sqrt{2}sin(2x-frac{pi}4)=frac{sqrt3}2\sin(2x-frac{pi}4)=frac{sqrt3}{2sqrt2}\sin(2x-frac{pi}4)=frac{sqrt3*sqrt2}{2sqrt2*sqrt2}\sin(2x-frac{pi}4)=frac{sqrt6}{4}\2x-frac{pi}4=arcsin(frac{sqrt6}4)+2pi n;nin Z\2x-frac{pi}4 = pi - arcsin(frac{sqrt6}4)+2pi n;nin Z\2x=frac{pi}4+arcsin(frac{sqrt6}4)+2pi n;nin Z\2x = frac{5pi}4 - arcsin(frac{sqrt6}4)+2pi n;nin Z$
$x=frac{pi}8+frac{1}2arcsin(frac{sqrt6}4)+pi n;nin Z\x = frac{5pi}8 - frac{1}2arcsin(frac{sqrt6}4)+pi n;nin Z$