Tanx-cotx / secx + cosecx = √2 / 2 x=?

(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