Use a half-angle formula to find the exact value of cos(7pi )/(8) cos(7pi )/(8)= square

Question

Answer 1

To find the exact value of

using a half-angle formula, we first need to express

in a form that allows us to apply the half-angle formula. The half-angle formula for cosine is:

We need to express

as

. Let

. Then:

Now, we can use the half-angle formula:

Next, we need to find

. Since

is in the fourth quadrant, where cosine is positive, and

, we have:

Substituting this value into the half-angle formula:

Simplify the expression inside the square root:

Rationalizing the denominator:

Thus, the exact value of

is:

Question