Question

cos(5π/12)

Answer 1

Well, all that really needs to be done is for you to enter this into a calculator. \[\frac{\sqrt3-1}{2 \sqrt2}\]

Answer 2

If you need to do it algebraically, here it is:

cos(5π/12) = cos(π/6 + π/4)
cos (a + b) = cos a cos b - sin a sin b
cos (π/6 + π/4) = cos π/6 cos π/4 - sin π/6 sin π/4

= √3 / 2 * √2 / 2 - 1/2 * √2 / 2
= √6 / 4 - √2 / 4