已知θ为锐角,求证:sinθ﹢cosθ<π/2

问题描述:

已知θ为锐角,求证:sinθ﹢cosθ<π/2

sinθ+cosθ=√2sin(θ+π/4)
∵0<θ<π/2
∴π/4<θ+π/4<3π/4
√2 /2<sin(θ+π/4)≤1
∴1<√2sin(θ+π/4)≤√2
即:1<sinθ+cosθ≤√2