### Cosine of multiples

The general formula for calculating the cosine of multiples was given by the French mathematician Viète

The latter term is alternately 1, 0, −1, 0, 1 and so on, so that half of the factors in the sum disappear.

##### Example 0

We know that cos (0) = 1 and see if the formula gives this also. We take *n* = 0 and get

The only term is

This result arises here because we have taken sin^{0}0 = 1.

##### Example 1

Now we want to see what happens with *n* = 1 and find

The two consecutive terms are then

so that only remains cos *x* = cos *x*.

##### Example 2

For *n* = 2 the formula yields the sum

The three consecutive terms are then

so that only remains

This is what we expected, because the addition formula for the cosine is

and as a direct result