当 θ∈（0,π/2)时,求证sinθ +cosθ ＜π/2如题_数学解答

当 θ∈（0,π/2)时,求证sinθ +cosθ ＜π/2
如题

人气：172 ℃　时间：2020-04-02 18:05:46

解答

sinθ+cosθ
=√2(√2/2*sinθ+√2/2cosθ)
=√2(sinθcosπ/4+cosθsinπ/4)
=√2sin(θ+π/4)
θ∈（0,π/2)
π/4