Question

tan 15
$\tan(15)$
​

Answer 1

Answer:

$\sf \tan(45°-30°)$

$\Large \sf \frac{\tan45° - \tan30°}{1+(tan45°×tan30°)}$

$\Large \sf \frac{1 - \frac{1}{√3}}{1 + \frac{1}{√3}}$

Now by rationalising,

$\Large \sf \frac{(1 - \frac{1}{√3})(1 - \frac{1}{√3})}{(1 + \frac{1}{√3})(1 - \frac{1}{√3})}$

$\Large \sf \frac{(1 - \frac{1}{√3})^{2}}{1 - \frac{1}{3}}$

$\Large \sf \frac{1+ \frac{1}{3} - \frac{2}{√3}}{1 - \frac{1}{3}}$

$\Large \sf {\frac{3+1-2√3}{3} × \frac{3}{2}}$

$\Large \sf \frac{4-2√3}{2}$

$\sf{2 - √3}$