Question

cos pi/12

Answer 1

Note that \[\frac{\pi}{3}-\frac{\pi}{4}=\frac{\pi}{12}\]You need to use the angle difference formulas:\[\cos(\alpha-\beta)=\cdots\]

Answer 2

cos π/12 = cos [(π/6) /2]
use the double angle formula
cos (π/6) = {cos [(π/6) /2] }^2 -1
(sqrt3) /2 = {cos [(π/6) /2] }^2 -1
[(sqrt3) /2]+1 = {cos [(π/6) /2] }^2
cos [(π/6) /2] = sqrt {[(sqrt3) /2]+1}

Very messy ... sorry :(