∵y=√(tanx-1)+log cosx
∴tanx-1≥0
tanx≥1
∴x∈[kπ+π/4,kπ+π/2)(k∈Z)
又∵cosx>0
∴x∈(2kπ-π/2,2kπ+π/2)(k∈Z)
综上,x∈[2kπ+π/4,2kπ+π/2)(k∈Z)
∴定义域为[2kπ+π/4,2kπ+π/2)(k∈Z)
∵y=√(tanx-1)+log cosx
∴tanx-1≥0
tanx≥1
∴x∈[kπ+π/4,kπ+π/2)(k∈Z)
又∵cosx>0
∴x∈(2kπ-π/2,2kπ+π/2)(k∈Z)
综上,x∈[2kπ+π/4,2kπ+π/2)(k∈Z)
∴定义域为[2kπ+π/4,2kπ+π/2)(k∈Z)