Question

Find the value of $\tan {15}^o$.

Answer 1

We have,

$\tan {15}^o$

$=\tan ({45}^o-{30}^o)$

$=\frac{\tan {45}^o-\tan {30}^o}{1+\tan {45}^o.\tan {30}^o}$

$=\frac{1-\frac{1}{\sqrt{3}}}{1+1.\frac{1}{\sqrt{3}}}$

$=\frac{\sqrt{3}-1}{\sqrt{3}+1}$.