Question

Prove: $\tan {70}^o-\tan {20}^o=2\tan {50}^o$

Answer 1

$\because {70}^o={50}^o+{20}^o$
$\therefore \tan {70}^o=\frac{\tan {50}^o+\tan {20}^o}{1-\tan {50}^o\tan {20}^o}$
or $\tan {70}^o-\tan {70}^o\tan {50}^o\tan {20}^o=\tan {50}^o+\tan {20}^o$
or $\tan {70}^o-\tan {20}^o=\tan {50}^o+\tan {50}^o=2\tan {50}^o[\because \tan {70}^o\tan {20}^o=\tan ({90}^o-{20}^o)\tan {20}^o=\cot {20}^o\tan {20}^o=1]$
∵70o=50o+20o