1
2(√2/2sinx+√2/2cosx)=1
sin(x+π/4)=1/2
x+π/4=π/6+2πn U x+π/4=5π/6+2πn
x=-π/4+π/6+2πn U x=-π/4+5π/6+2πn
x=-π/12+2πn,n∈z U x=7π/12+2πn,n∈z
2
2(√2/2sinx-√2/2cosx)=1
sin(x-π/4)=1/2
x-π/4=π/6+2πn U x-π/4=5π/6+2πn
x=π/4+π/6+2πn U x=π/4+5π/6+2πn
x=5π/12+2πn,n∈z U x=13π/12+2πn,n∈z
3
√2cosπ/4cosx+√2sinπ/4sinx-cosx=0,5
√2*1/√2*cosx+√2*1/√2*sinx-cosx=0,5
cosx+sinx-cosx=1/2
sinx=1/2
x=π/6+2πn,n∈z U x=5π/6+2πn,n∈z
Xy+2(x-y)=10 xy=z z+2t=10 z+2t=10
5xy-3(x-y)=11 (x-y)=t ⇔ 5z-3t=11 -13t =-39 t=3
z=4
xy=4 (3+y)y=4 y²+3y-4=0 ⇔ y1=-4 y2=1
(x-y)=3 ⇔x=3+y ⇔ x=3+y x1=-1 x2=4
проверка
x1=-1 у1=-4
xy+2(x-y)=10 (-1)(-4)+2(-1-(-4))=10 верно
5xy-3(x-y)=11 5(-1)(-4)-3(-1-(-4))=11 верно
x2=4 у2=1
xy+2(x-y)=10 (4)(1)+2(4-1)=10 верно
5xy-3(x-y)=11 5(4)(1)-3(4-(1))=11 верно