求证:cos(cosx)>sin(sinx),

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求证:cos(cosx)>sin(sinx),
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求证:cos(cosx)>sin(sinx),
求证:cos(cosx)>sin(sinx),

求证:cos(cosx)>sin(sinx),
首先sin(x)+cos(x) = √2·sin(x+π/4) ≤ √2 < π/2, 故sin(x) < π/2-cos(x).
同理可得sin(x) < π/2+cos(x), 于是-π/2 < sin(x) < π/2-|cos(x)| ≤ π/2.
由sin(x)在[-π/2,π/2]上严格单调递增, 有sin(sin(x)) < sin(π/2-|cos(x)|) = cos(|cos(x)|) = cos(cos(x)).