Pre Cal
posted by Kara .
cos 75 deg

cos(75) = cos(9015) = sin(15)
sin(15) = √((1cos(30))/2)
= √((1√3/2)/2)
= 1/2 √(2√3)
or
sin(15) = sin(4530)
= sin45cos30  cos45sin30
= 1/√2(√3/2  1/2)
= (√31)/(2√2)
I'll leave it to you to demonstrate that the two values are equal . . .