Question

Find the value of $\tan {20}^0+\tan {25}^0+\tan {25}^0\tan {20}^0$.

Answer 1

$\tan ({20}^0+{25}^0)=\tan {45}^0=1$
$\therefore \frac{\tan {20}^0+\tan {25}^0}{1-\tan {20}^0\tan {25}^0}=1$
or $\tan {20}^0+\tan {25}^0=1-\tan {20}^0\tan {25}^0$
$\therefore \tan {20}^0+\tan {25}^0+\tan {20}^0\tan {25}^0=1$