Question

Решите уравнение.
2cos2x+ cosx = sin(3П/2+x)-2

Answer 1

$2cos2x+ cosx = sin( \frac{3 \pi }{2} +x)-2$
$2cos2x+ cosx = -cosx-2$
$2(2cos^{2}x-1)+ cosx +cosx+2=0$
$4cos^{2}x-2+2cosx+2=0$
$4cos^{2}x+2 cosx=0$
$2 cosx(2 cosx+1)=0$
$2 cosx=0$
$cosx=0$
$x= \frac{\pi}{2}+ \pi n,$  n∈Z;
$2cosx=-1$  ⇒  $cosx=- \frac{1}{2}$
$\left \{ {{x=\frac{2 \pi }{3} +2 \pi n} \atop {x= -\frac{2 \pi }{3} +2 \pi n}} \right.$   n∈Z;