Question

Find the exact value of tan 5pi/12

Answer 1

tan( 5π/12) =
tan(3π/12 + 2π/12) =
tan( π/4 + π/6) =
[ tan(π/4) + tan(π/6) ] / [ 1 - tan(π/4)•tan(π/6)] =
[ 1 + 1/√3 ] / [ 1 - 1 • 1/√3] =
[ (3 + √3) /3 ] / [ (3 - √3) / 3] =
(3 + √3) / (3 - √3) =
(3 + √3)² / (9 - 3) =
(9 + 6√3 + 3) / 6 =
(12 + 6√3) / 6 =
2 + √3

Answer 2

medal