Which is greater cos(sinx) or sin(cosx)

[Zargon]

Which is greater cos(sinx) or sin(cosx)

Through graphing and using a table of values i have determined that cos(sinx) is greater, but i do not know how to do it algebraically. Any help is appreciated.
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Edited by stapel. Reason for edit: Copying question from subject line into post.

[nona.m.nona]

The proof involves using trig identities, and gets pretty nasty. See if you can follow what was done on Nick's Mathematical Puzzles.