How can I determine the exact values for tan75?

1 Answer
May 28, 2015

tan(75^@) = tan (90^@ - 15^@) = cot(15^@) = 1/(tan(15^@)

tan(15^@) = tan(30^@/2)

= (sin(30^@))/(1+cos(30^@))

= (1/2)/(1+sqrt(3)/2)

= 1/(2+sqrt(3)

So
tan(75^@) = 1/tan(15^@) = 2+sqrt(3)