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

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SUMMARY

The discussion focuses on proving the trigonometric identity tan(2A) = 2tan(A)/(1 - tan^2(A)). Participants explore the right-hand side of the equation, starting with the expression 2(sinA/cosA) and simplifying it to 2sinA/cos(2A). The conversation highlights the need for clarity in mathematical notation and emphasizes the importance of recognizing the identity for sin(2A) in the proof process. The participants express uncertainty about the next steps in the proof.

PREREQUISITES
  • Understanding of trigonometric identities, specifically tan(2A) and sin(2A).
  • Familiarity with the sine and cosine functions and their relationships.
  • Basic algebraic manipulation skills, particularly with fractions and trigonometric expressions.
  • Knowledge of the Pythagorean identity sin^2(A) + cos^2(A) = 1.
NEXT STEPS
  • Study the derivation of the double angle formulas for sine and cosine.
  • Learn how to manipulate trigonometric identities using algebraic techniques.
  • Practice proving other trigonometric identities to strengthen understanding.
  • Explore the implications of the Pythagorean identity in trigonometric proofs.
USEFUL FOR

Students studying trigonometry, educators teaching trigonometric identities, and anyone looking to enhance their skills in mathematical proofs and algebraic manipulation.

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.
 
Last edited:

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