Let α be an acute angle and prove: sin α + cos α
α∈(0,π/2)
α+π/4∈(π/4,3π/4)
sinα+cosα
=√2(√2/2*sinα+√2/2*cosα)
=√2(sinαcosπ/4+cosαsinπ/4)
=√2sin(α+π/4)
sin(α+π/4)∈[√2/2,√2]
That is sin α + cos α ∈ [√ 2 / 2, √ 2]
Because √ 2
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