sinx + cosx =√2 = √2·sin[x + (π/4)],∴sin[x + (π/4)] = 1,∴x + (π/4) = 2kπ + (π/2),k∈Z∴x/2 = kπ + (π/8),而tan(x/2) = tan[kπ + (π/8)] = tan(π/8)>0∵1 = tan(π/4) = 2tan(π/8)/{1 - [tan(...