Proving tan2A = 2tanA/1-tan^2A: A Trig Identity Example

AI Thread Summary
The discussion focuses on proving the trigonometric identity tan(2A) = 2tan(A)/(1 - tan^2(A). The user attempts to manipulate the right-hand side using sine and cosine relationships but expresses confusion about the next steps. Another participant suggests clarifying the expression involving sin(2A) and highlights the need for clearer notation. The conversation emphasizes the importance of proper formatting in mathematical expressions to avoid misunderstandings. The thread illustrates common challenges faced when proving trigonometric identities.
TheRedDevil18
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Homework Statement


Prove the following:

tan2A=2tanA/1-tan^2A

Homework Equations





The Attempt at a Solution



Took the right hand side:

=2(sinA/cosA) / 1-(sin^2A/cos^2A)
=2sinA/cosA /cos^2A-sin^2A/cos^2A
=2sinA/cos2A /cosA/1

Dont know what to do next?
 
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TheRedDevil18 said:

Homework Statement


Prove the following:

tan2A=2tanA/1-tan^2A

Homework Equations


The Attempt at a Solution



Took the right hand side:

=2(sinA/cosA) / 1-(sin^2A/cos^2A)
=2sinA/cosA /cos^2A-sin^2A/cos^2A
=2sinA/cos2A /cosA/1

Dont know what to do next?

What's an identity for sin(2A)? And I hope 2sinA/cos2A /cosA/1 means (2sin(A))/(cos(2A)/cos(A)) what you've written is not at all clear.
 
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