sinx+cosx=sinxcosx+1

 Sinx+cosx=sinxcosx+1 ;2(Sinx+cosx)= 2sinxcosx+2 ;2(Sinx+cosx)=(sinx+cosx)²+1;(sinx+cosx)²-2(Sinx+cosx)+1 =0 ;(sinx +cosx -1)² =0;sinx +cosx =1 ; * * * 1/√2sinx +1/√2cosx =1/√2 ⇔(cosx*cosπ/4+sinx*sinπ/4) = 1/√2 * * * cos(x -π/4) =1/√2 ;x -π/4 =± π/4+2πn , n∈Z.x = π/4 ± π/4+2πn , n∈Z. x₁ =2πn ; x₂ = π/2 +2πn , n∈Z.ответ: 2πn ; π/2 +2πn , n∈Z.