1. ## Double/half angle formula

Stuck with this one.
I am thinking half angle formulae but cant get started
Im asked to use the top identity to solve the bottom problem

2. I think the formula is:

$tan(2\theta)=\frac{2tan(\theta)}{1-tan^2(\theta)}$

So,

$tan(\frac{\pi}{4})=\frac{2tan(\frac{\pi}{8})}{1-tan^2(\frac{\pi}{8})}$

3. Thanks
How would I work out the values?

4. Hmm, are you sure you wrote the rest of the question correctly?

$sin(\frac{\pi}{8})=\frac{\sqrt{2-\sqrt{2}}}{2}$

and,

$cos(\frac{\pi}{8})=\frac{\sqrt{2+\sqrt{2}}}{2}$

so,

$tan(\frac{\pi}{8})=\frac{\frac{\sqrt{2-\sqrt{2}}}{2}}{\frac{\sqrt{2+\sqrt{2}}}{2}}=\sqrt{ 3-2\sqrt{2}}$