Question

tan80+tan65+tan35=tan80*tan658tan35 prove

Answer 1

\[\tan(80+65 + 35) = \dfrac{\tan(80) + \tan(65) + \tan(35) - \tan(80)\tan(65)\tan(35)}{1- \tan(80)\tan(65) - \tan(65)\tan(35) - \tan(80)\tan(35)}\]Since the LHS is zero, the RHS must be zero.

Answer 2

This means that the numerator\[\tan(80) + \tan(65) + \tan(35) - \tan(80)\tan(65)\tan(35)=0\]