Evaluate and simplify tan 5π/12.

Answer 1

tan 5π/12 or tan 75°

I will use degrees ...
tan 75 = tan(30 + 45)
= (tan30+tan45)/( 1 - tan30tan45)
= (1/√3 + 1)/( 1 - 1/√3) , multiply top and bottom by √3
= (1 + √3)/√3 - 1)