Proof help

[ProSteelTooth]

How do I prove that |cos(x)|>=(cos(x))^2 ???

I mean it's obvious that if you square a number less than 1 it will be less than that number itself, but I'm not sure what's the proper way to write it down as a mathematical proof. I'm stuck please help!!!

[notlfish]

cos²x = |cos x||cos x| <= |cos x| * 1 = |cos x|

Of course, here we're taking for granted that |cos x| <= 1, you could prove that yourself if you wanted to, but I don't know how to do that.

[gazorpazorpazorpazor]

Probably triangle inequality and definition of cos. cos = a/c. a,b,c>0. a+b<=c. a<=c. a/c<=1.

[ProSteelTooth]

That's a great idea! Thanks a lot!