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Addition formula for the cosine

For the addition of arguments in the cosine applies

 


Explanation

We start from the definition of the cosine

Then applies

Substitution with Euler's formula gives

so that

 


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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