Proving Trigonometric Identities

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SUMMARY

The forum discussion focuses on proving the trigonometric identity sinΘ tanΘ = cosΘ sec²Θ - cosΘ. The solution begins with the left side, transforming sin(θ)tan(θ) into tan²(θ)cos(θ) using the identity tan(θ) = sin(θ)/cos(θ). The proof utilizes the fundamental identity tan²(θ) = sec²(θ) - 1 to simplify the expression further, confirming the identity holds true.

PREREQUISITES
  • Understanding of trigonometric identities, specifically sin, cos, and tan.
  • Familiarity with the Pythagorean identity: tan²(θ) + 1 = sec²(θ).
  • Basic algebraic manipulation skills to simplify trigonometric expressions.
  • Knowledge of how to manipulate fractions and apply identities in proofs.
NEXT STEPS
  • Study the derivation and applications of the Pythagorean identity in trigonometry.
  • Learn how to prove other trigonometric identities using similar techniques.
  • Explore the unit circle and its relationship to trigonometric functions.
  • Practice solving more complex trigonometric equations and identities.
USEFUL FOR

Students studying trigonometry, mathematics educators, and anyone looking to strengthen their understanding of trigonometric identities and proofs.

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Homework Statement



Prove (using the left side):

sinΘ tanΘ = cosΘ sec^2Θ - cosΘ

Homework Equations





The Attempt at a Solution

 
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[tex]sin(\theta)tan(\theta)= \frac{sin(\theta)}{cos(\theta)}tan(\theta)cos(\theta)= \tan^2(\theta)cos(\theta)[/tex]

Now use the fact that [itex]tan^2(\theta)= sec^2(\theta)- 1[/itex].
 

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