(tgx-ctgx)/(1/cosx+1/sinx)=√2/2
(sinx/cosx-cosx/sinx):(sinx+cosx)/(sinxcosx)=√2/2
(sin²x-cos²x)/(sinxcosx)*(sinxcosx)/(sinx+cosx)=√2/2
(sinx-cosx)(sinx+cosx)*1/(sinx+cosx)=√2/2
sinx-cosx=√2/2
√2*(sinx*1/√2-cosx*1/√2)=√2/2
sin(x-π/4)=1/2
x-π/4=π/6+2πk U x-π/4=5π/6+2πk
x=π/4+π/6+2πk U x=π/4+5π/6+2πk
x=5π/12+2πk U x=13π/12+2πk,k∈z