Решить систему:
x-y=Pi/2
cosx-cosy = - корень из 2

Решениеx - y = π/2cosx - cosy = - √2x = π/2 + y cos(π/2 + y) - cosy = - √2- siny - cosy = - √2-(cosy + siny) = - √2- (√2cos(π/4 - y) = - √2cos(y - π/4) = 1y - π/4 = 2πk, k∈Zy = π/4 + 2πk, k∈Zx = π/2 + π/4 + 2πk, k∈Zx = 3π/4 + 2πk, k∈ZОтвет: x = 3π/4 + 2πk, k∈Z ; y = π/4 + 2πk, k∈Z 

 { x - y =π/2 ; cosx - cosy =√2  ⇔   { x - y =π/2 ; - 2sin(x-y)/2*sin(x+y)/2  =√2 .{ x - y =π/2 ; - 2sinπ/4*sin(x+y)/2  =√2 . - 2sinπ/4*sin(x+y)/2  =√2 ;-2*(1/√2)*sin(x+y)/2 =√2 ;sin(x+y) = -1;x+y = π+2π*k  , k∈ Z .{x+y = π+2π*k  , k∈ Z ;   x-y =π/2 ⇔ {2x =π+2π*k +π/2 ; 2y = π+2π*k -π/2. {x =3/4π+ π*k    ;  y = π/4+ π*k  , k ∈Z.ответ :   x =3/4π+ π*k , k ∈Z  ,   y = π/4+ π*k  , k ∈Z.