Question

How do you find the exact value `cos ((23pi)/12)`?

Answer 1

That depends on what you already know.

If you have the sum and difference identitiy, find two special angles whose sum or difference is `(23 pi)/12`

`(2 pi)/12 + (21 pi)/12` reduces to `pi/6 + (7 pi)/4` so that will work.

Or
`(3 pi)/12 + (20 pi)/12` reduces to `pi/4 + (5 pi)/3` so that would work too.

If you have the half angle identity, you could use

`cos ((23pi)/12) = cos (1/2((23pi)/6))`