Question

cos 75 deg

Answer 1

cos(75) = cos(90-15) = sin(15)

sin(15) = √((1-cos(30))/2)
= √((1-√3/2)/2)
= 1/2 √(2-√3)

or

sin(15) = sin(45-30)
= sin45cos30 - cos45sin30
= 1/√2(√3/2 - 1/2)
= (√3-1)/(2√2)

I'll leave it to you to demonstrate that the two values are equal . . .