Question

Prove that:

$\tan {20}^o+\tan {25}^o+\tan {20}^o.\tan {25}^o=1$.

Answer 1

We know,

$\tan {45}^o=1$

or, $\tan ({25}^o+{20}^o)=1$

or, $\frac{\tan {25}^o+\tan {20}^o}{1-\tan {20}^o.\tan {25}^o}=1$

or, $\tan {25}^o+\tan {20}^o+\tan {25}^o.\tan {20}^o=1$.