Корень из двух sinx + корень из двух cosx=1 корень из двух sinx - корень из двух cosx=1 корень из двух cos(pi\4-x) -cosx = 0.5 даже если только одно, все равно пишите.
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
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