Please Help.

[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.

1. The problem statement, all variables and given/known data

Prove that,

tan3A + tan2A + tanA = tan3Atan2AtanA

3. 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.