5pi/12 = 3pi/12 + 2pi/12 = pi/4 + pi/6
sin(a + b) => sin(a)cos(b) + sin(b)cos(a)
cos(a + b) => cos(a)cos(b) - sin(a)sin(b)
sin(5pi/12) =>
sin(3pi/12 + 2pi/12) =>
sin(pi/4 + pi/6) =>
sin(pi/4)cos(pi/6) + sin(pi/6)cos(pi/4) =>
(sqrt(2)/2) * (sqrt(3)/2) + (1/2) * (sqrt(2)/2) =>
(sqrt(2)/4) * (1 + sqrt(3))
cos(5pi/12) =>
cos(pi/4 + pi/6) =>
cos(pi/4)cos(pi/6) - sin(pi/4)sin(pi/6) =>
(sqrt(2)/2) * (sqrt(3)/2) - (sqrt(2)/2) * (1/2) =>
(sqrt(2)/4) * (sqrt(3) - 1)
tan(5pi/12) =>
sin(5pi/12) / cos(5pi/12) =>
(sqrt(2)/4) * (sqrt(3) + 1) / ((sqrt(2)/4) * (sqrt(3) - 1)) =>
(sqrt(3) + 1) / (sqrt(3) - 1) =>
(sqrt(3) + 1)^2 / (3 - 1) =>
(3 + 2 * sqrt(3) + 1) / 2 =>
(4 + 2 * sqrt(3)) / 2 =>
2 + sqrt(3)
csc(5pi/12) =>
1 / sin(5pi/12) =>
4 / (sqrt(2) * (sqrt(3) + 1)) =>
4 * sqrt(2) * (sqrt(3) - 1)) / (2 * (3 - 1)) =>
4 * sqrt(2) * (sqrt(3) - 1)) / (2 * 2) =>
sqrt(2) * (sqrt(3) - 1)
sec(5pi/12) =>
1/cos(5pi/12) =>
4 / (sqrt(2) * (sqrt(3) - 1)) =>
4 * sqrt(2) * (sqrt(3) + 1)) / (2 * (3 - 1)) =>
sqrt(2) * (sqrt(3) + 1)
cot(5pi/12) =>
1/tan(5pi/12) =>
1 / (2 + sqrt(3)) =>
(2 - sqrt(3)) / (4 - 3) =>
2 - sqrt(3)
