Prove that? tanx+tan2x+tan3x=tanx.tan2x.tan3x

1 Answer
Aug 9, 2018

Please see The Explanation.

Explanation:

We have, tan3x=tan(x+2x)tan3x=tan(x+2x),

=(tanx+tan2x)/(1-tanxtan2x),=tanx+tan2x1tanxtan2x,

i.e., tan3x=(tanx+tan2x)/(1-tanxtan2x)i.e.,tan3x=tanx+tan2x1tanxtan2x.

:. (1-tanxtan2x)tan3x=tanx+tan2x,

or, tan3x-tanxtan2xtan3x=tanx+tan2x

rArr tan3x=tanx+tan2x+tanxtan2x