Pre- calc question

Question

Find the exact value of

cos(2 cos^-1√3/2)

Answer 1

the angle whose cosine is sqr3/2 is 30 degrees or pi/6 radians

double it and it's 60 degrees or pi/3 radians 2cos^-1(sqr3/2) = 60 or pi/3

cos60 = cospi/3 = 1/2 = 0.5

1/2 or 0.5 is the solution, exactly

cos^-1(sqr3/2)= 30 or -30 or 30+n360 or -30+n360 where n is any integer. but double -30 and that's -60 and cos(-60) is also 1/2. so the answer doesn't change, no matter what integer n is. Just let n=0 to simplify.