Question

Question #01ea9

Answer 1

`tan (pi/8) = 1/(1+sqrt(2))`

Explanation:

We have that:

`tan (pi/8) = tan(1/2*pi/4)`

Using the half angle formulae:

`tan (alpha/2) = frac sin alpha (1+cos alpha)`

`tan (pi/8) = frac sin(pi/4) (1+cos(pi/4)) = frac (sqrt(2)/2) (1+sqrt(2)/2) = 1/(1+sqrt(2))`