Question

$left { {{cosx= frac{1}{2} } atop {sinx+cosx textgreater 0}} right.$

Answer 1

{cosx=1/2⇒x=-π/3+2πk U x=π/3+2πk,k∈z
{sinx+cosx>0⇒cos(π/2-x)+cosx>0⇒2cosπ/4*cos(π/4-x)>0⇒√2cos(x-π/4)>0⇒
cos(x-π/4)>0⇒-π/2+2πk<x-π/4<π/2+2πk⇒-π/4+2πk<x<3π/4+2πk,k∈z
Ответ x=π/3+2πk,k∈z