Question

How do you use the half angle identity to find `tan (pi/8)`?

Answer 1

By the half-angle identity

`tan(theta/2)={sin theta}/{1+cos theta}`,

we have

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

---

I hope that this was helpful.