Solve cot cot5pi/125pi/12

Question

Solve cot
`cot5pi/12`5pi/12

Answer 1

cot(5pi/12) = tan(pi/12)

tan(x/2) = (1 - cos(x)) / sin(x))

tan(pi/12) = tan((pi/6)/2) = (1 - cos(pi/6)) / sin(pi/6))

sin(pi/6) = 1/2

cos(pi/6) = sqrt(3) / 2

so...

tan(pi/12) = (1 - sqrt(3)/2) / (1/2) = 2 - sqrt(3)