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

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    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.