若 cos(sinx) > sin(cosx)
則 cos(sinx) - sin(cosx) > 0
=> cos(sinx) - cos(π/2 - cosx) > 0
=> 2 * sin[(π/4) + (1/2) * (sinx - cosx) ] *
sin[(π/4) - (1/2) * (sinx - cosx)] > 0 ...........(1)
因為 |sinx - cosx| = |√2 * sin(x - π/4)| ≦ √2 < π/2
所以 -π/2 < (sinx - cosx) < π/2
=> -π/4 < (sinx - cosx)/2 < π/4
=> 0 < π/4 + (1/2) * (sinx - cosx) < π/2
=> sin[(π/4) + (1/2) * (sinx - cosx) ] > 0 ...........(2)
同理，
sin[(π/4) - (1/2) * (sinx - cosx) ] > 0 ...........(3)
由(2)、(3)可推得(1)。
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