What is the exact value of the cos of 23pi/12?

Question

(Twenty-three pi over 12, which is = to 345 degrees.)

Thank you,
Roger

Answer 1

cos 23π/12 = cos 345°
= cos 15° ( we are 15° from the x-axis in quadrant IV, and the cosine in IV is positive)

I know cos 2A = 2cos^2 A - 1
or
cos 30° = 2cos^2 15 - 1
√3/2 + 1 = 2cos^2 15
(√3 + 2)4 = cos^2 15
cos 15 = [√(√3+2)]/2