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Addition formula for the cosine

For the addition of arguments in the cosine applies

 

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Explanation

We start from the definition of the cosine

Then applies

Substitution with Euler's formula gives

so that

 

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Example 1

For cos (2x) applies

cos (2x) = cos (x + x) = cos x cos x − sin x sin x = cos² x − sin²x

 

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