let's first handle 75 degrees
tan75 = tan(30+45) , skipping the degree symbols
= (tan30 + tan45)/(1 - tan30tan45)
= (1/sqr3 + 1)/(1 - (1/sqr3)(1))
= (sqr3 + 1)/(sqr3 - 1)
tan 75 = 2tan(75/2)/( 1 - tan^2 (75/2) )
let tan(75/2) = x for easier typing
(sqr3 + 1)/(sqr3 - 1) = 2x/(1 - x^2)
argghh, I used the quadratic formula and got
x = (2(sqr( 2 + sqr3) ) - 1 )/(2 + sqr3)
= appr .7673
tan75\2
3 answers
15-8√3
√2+√3