Cos(x/2) +sin(x/2) = -1 ; * * * sinπ/4 =cosπ/4 =1/√2 * * *
(1/√2)*cos(x/2)+(1/√2) *sin(x/2) = -1/√2 ;
cos(x/2)*cos(π/4)+ sin(x/2)*sin(π/4) = -1/√2 ;
* * * cos(α -β) =cosα*cosβ - sinα*sinβ * * *
cos(x/2 -π/4) = -1/√2 ;
x/2 -π/4 = ±(π -π/4) +2πn , n∈Z ;
x/2 =π/4 ±3π/4 +2πn , n∈Z ;
x =π2 ±3π/2 +4πn , n∈ Z .
или
x₁ = - π +4πn , n∈ Z .
x₂ = 2π +4πn , n∈ Z .
ответ : - π +4πn , 2π +4πn , n∈ Z .