令f(α)=sinα-cosα
f(α)=sinα-cosα=(√2)sin[α-(π/4)]
f(α)=0
sin[α-(π/4)]=0
α-(π/4)=2kπ或α-(π/4)=2kπ+π
α=2kπ+(π/4)或α=2kπ+(5π/4)
k=-1,α=-7π/4或α=-3π/4
在区间[-2π,0]上,至少有一个角α,使得sinα=cosα.
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