Simplifying Trigonometric Expressions

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SUMMARY

The discussion centers on simplifying the trigonometric expression (Sin 2θ / sinθ) - (cos 2θ / cos θ) = Sec θ. Participants utilized the identity sin(2θ) = 2sinθ cosθ to rewrite the expression, leading to sinθ cosθ - cos²θ / cosθ = Sec θ. The conversation emphasizes the importance of applying trigonometric identities correctly and verifying calculations to avoid errors.

PREREQUISITES
  • Understanding of trigonometric identities, specifically sin(2θ) and cos(2θ).
  • Familiarity with the concept of secant (Sec θ) in trigonometry.
  • Basic algebraic manipulation skills for simplifying expressions.
  • Knowledge of how to reduce fractions in mathematical expressions.
NEXT STEPS
  • Study the derivation and application of trigonometric identities, focusing on double angle formulas.
  • Practice simplifying complex trigonometric expressions using various identities.
  • Learn how to convert between different trigonometric functions, such as from sine and cosine to secant.
  • Review common mistakes in trigonometric simplifications and how to avoid them.
USEFUL FOR

Students studying trigonometry, educators teaching trigonometric identities, and anyone looking to enhance their skills in simplifying trigonometric expressions.

striker7770
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Homework Statement



(Sin 2θ / sinθ) - (cos 2θ/ cos θ) = Sec θ

just trying to match one side to the other

Homework Equations



all trig identities


The Attempt at a Solution



broke down sin2θ into 2sinθ cosθ then reduced the sinθ in the denominator

giving me
sinθ cosθ - cos2θ / cosθ = Secθ

thanks
 
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striker7770 said:

Homework Statement



(Sin 2θ / sinθ) - (cos 2θ/ cos θ) = Sec θ

just trying to match one side to the other

Homework Equations



all trig identities

The Attempt at a Solution



broke down sin2θ into 2sinθ cosθ then reduced the sinθ in the denominator

giving me
sinθ cosθ - cos2θ / cosθ = Secθ

thanks

You are on the right track. It should be clear to you that the next step is to express cos(2t) as in terms of cos(t). What trig identity do you know that will do that?

Oh, and double check your expression, you may have made a silly math error there.
 

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