How to Prove tan3A + tan2A + tanA Equals tan3Atan2AtanA?

[udaibothra]

Hello Everyone,

I'm doing my math in advance so I came across a Trigonometry question I came across in my textbook. I did make some progress but I do not know how to go about it further.

Homework Statement

Prove that,

tan3A + tan2A + tanA = tan3Atan2AtanA

The Attempt at a Solution

I did simplify tan3A as- tan(2A+A) and then tried going about it. I just need someone to spur me on to the right approach and not provide the answer necessarily.

 

[Mentallic]

Prove that,

tan3A + tan2A + tanA = tan3Atan2AtanA

But I can't...

...since it's generally not true!

The expansion of tan(A+B) is given by $$tan(A+B)=\frac{tanA+tanB}{1-tanAtanB}$$ but if you know the expansion of sin(A+B) and cos(A+B) then $$tan(A+B)=\frac{sin(A+B)}{cos(A+B)}$$

 

[HallsofIvy]

As Mentallic says, you cannot "prove" this because it is not true. For a counter example, take practically any values for A, say "A= 1". Is it possible that the problem was not to "prove an identity" but to solve for a value of A that makes the equation true?

 

[udaibothra]

Thank You! Must have been a typing error in the book. Yes, I do know the expansion of tan(A + B) Thnks anyways. I'll re-check the question and get back to you.