Explore BrainMass

Explore BrainMass

    Real analysis

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    29.2 Prove that |cos x - cos y| ≤ |x - y| for all x, y in R

    © BrainMass Inc. brainmass.com February 24, 2021, 2:36 pm ad1c9bdddf


    Solution Preview

    See attachment

    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:
    ( 1)
    We start from the basic formulas:
    ( 2)
    ( 3)
    By subtracting first equality from the second one, we will have
    ( 4)
    We denote now
    ( 5)
    By adding the 2 equations, one ...

    Solution Summary

    This is a proof regarding cosx and cosy for x, y in R.