Can someone tell me how to get the pie6 and how to go from t

Can someone tell me how to get the pie/6 and how to go from the 3rd equation to the last(answer). I feel these are basic rules from earlier math, but I don\'t remember. Thanks

Solution

As cos 2x = 1 - 2sin^2 x

and cospi/6 = cos 30 = sqrt(3)/2

sin(pi/12) = sin(pi/6/2) = sqrt[(1 - cospi/6)/2] = sqrt[(1 - sqrt(3)/2)/2] = sqrt[2 - sqrt(3)]/2