Question

ПОМОГИТЕ РЕШИТЬ
$sqrt{3}$ sin 2х + cos 2x = $sqrt{2}$

Answer 1

√3*sin2x+cos2x=√2 | : 2
$frac{ sqrt{3}*sin2x }{2} + frac{cos2x}{2}= frac{ sqrt{2} }{2}$
$frac{ sqrt{3} }{2}*sin2x+ frac{1}{2}*cos2x= frac{ sqrt{2} }{2}$
$cos frac{ pi }{6} *sin2x+sin frac{ pi }{6}*cos2x= frac{ sqrt{2} }{2}$
$sin(2x+ frac{ pi }{6} )= frac{ sqrt{2} }{2}$
$2x+frac{ pi }{6}=+-arccos frac{ sqrt{2} }{2}+2 pi n,$n∈Z
$2x+ frac{ pi }{6} =+- frac{ pi }{4} +2 pi n,$n∈Z
$2x=+- frac{ pi }{6}- frac{ pi }{4}+2 pi n,$n∈Z | : 2
$x=+- frac{ pi }{12}- frac{ pi }{8} + pi n,$n∈Z