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

1 Answer
Ratnaker Mehta
Aug 9, 2018

Please see The Explanation.

Explanation:

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

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

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

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

# or, tan3x-tanxtan2xtan3x=tanx+tan2x#

# rArr tan3x=tanx+tan2x+tanxtan2x#

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