sinθ+cosθ=√2sin(θ+π/4),
当θ∈(0,π/2)时,θ+π/4∈(π/4,3π/4),则sin(θ+π/4)∈(√2/2,1],
则:√2sin(θ+π/4)∈(1,√2],则x∈(0,1/2] (最后用对数单调性求解)