Is This A Correct/Sufficient Proof

[Sylvester Sly]

Homework Statement

Which is greater cos(sin(x)) or sin(cos(x)), determine with proof.

The Attempt at a Solution

http://img21.imageshack.us/img21/5193/proof1ii.jpg
http://img109.imageshack.us/img109/8678/proof2w.jpg

 

[Mark44]

Something you asserted early on is not true - that f(g(x)) = g(f(x)). I stopped reading after that.

 

[Sylvester Sly]

Something you asserted early on is not true - that f(g(x)) = g(f(x)). I stopped reading after that.

I was doing proof by contradiction. In order to prove f(g(x)) =/= g(f(x)) i started off by letting f(g(x)) = g(f(x)) and working from there.

 

[diazona]

I was doing proof by contradiction. In order to prove f(g(x)) =/= g(f(x)) i started off by letting f(g(x)) = g(f(x)) and working from there.

You would have been doing a proof by contradiction if you said you were doing a proof by contradiction. The way you've written it, you're just asserting (without justification) something that is not even true.

Other than that, it seems reasonable...

 

[Mark44]

If you're doing a proof by contradiction, you don't start with "therefore ..." - You start by assuming the thing you want to contradict.

Also, in the same line you have "Therefore g(f(x)) = f(g(x)) cos(sin(x))". It looks like you omitted part of what you wanted to say.

 

[HallsofIvy]

If you're doing a proof by contradiction, you don't start with "therefore ..." - You start by assuming the thing you want to contradict.

Also, in the same line you have "Therefore g(f(x)) = f(g(x)) cos(sin(x))". It looks like you omitted part of what you wanted to say.

I assumed that was a typos for "g(f(x))= f(g(x))= cos(sin(x))". But, in any case, if the problem was to determine which was larger, I don't see what a proof by contradiction that they are not equal would accomplish.