Question

Find the value of tan $\frac{\pi }{8}$.

Answer 1

We know that tan x = $x=\frac{1-cos2x}{\text{sin~2x}}$

$\therefore \text{tan}\frac{\pi }{8}=\frac{1-\text{cos~2}\frac{\pi }{8}}{sin2\frac{\pi }{8}}\Rightarrow \text{tan}\frac{\pi }{8}=\frac{1-cos\frac{\pi }{4}}{sin\frac{\pi }{4}}\Rightarrow tan\frac{\pi }{8}=\frac{1-\frac{1}{\sqrt{2}}}{\frac{1}{\sqrt{2}}}=\sqrt{2}-1$