29.2 Prove that |cos x - cos y| ≤ |x - y| for all x, y in R© BrainMass Inc. brainmass.com November 24, 2021, 11:27 am ad1c9bdddf
29.2 Prove that |cos x - cos y| ≤ |x - y| for all x, y in R.
In order to prove the above statement, we need to prove first some trigonometric basic formulas.
1) Let's prove the identity:
We start from the basic formulas:
By subtracting first equality from the second one, we will have
We denote now
By adding the 2 equations, one ...
This is a proof regarding cosx and cosy for x, y in R.