Prove that

( x^100) / e^(x^70) + e^(x^70) /(x^100) > 2

for every positive x.

Prove that

cos 20 =/= a/b where a and b are integers .

Nice questions i did them i just wanted to see other solutions.

This should be easy for a lot of you i looked around the forum there are a lot of beautiful mathematicians around.