Question

How can I determine the exact values for tan75?

Answer 1

`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)`