# Real analysis

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

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##### Solution Summary

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

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

Solution:

In order to prove the above statement, we need to prove first some trigonometric basic formulas.

1) Let's prove the identity:

( 1)

Proof:

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 ...

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