求证：cos(sinx)大于sin(cosx)

老外的办法,你顺便学英语了
We have to prove :
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)
If we could prove that both the factors on the left hand side of (1) are positive then the result obtained above (1) is proved.
Since | sinx - cosx | = | √2 sin (x-π/4) | ≤ √2 We have - π/2 => - π/4 So that 0 And therefore sin [ (π/4) + (1/2).(sinx - cosx) ].> 0 ie Positive.
Similarly we can prove that
sin [ (π/4) - (1/2).(sinx - cosx) ] > 0 ie Positive
Hence (1) is true..Proved.