Check expression equivalent to

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SUMMARY

The discussion centers on simplifying the expression "sec theta - sec theta (sin^2 theta)" to find its equivalent form. Participants confirm that the expression simplifies to "cos theta" after substituting "sin^2 theta" with "1 - cos^2 theta" and factoring out "1/cos theta". A correction is noted regarding the negative sign in the expression "-cos^2 theta/cos theta", which should not be present. The consensus is that the final equivalent expression is indeed "cos theta".

PREREQUISITES
  • Understanding of trigonometric identities, specifically "sin^2 theta + cos^2 theta = 1"
  • Familiarity with the secant function and its relation to cosine, "sec theta = 1/cos theta"
  • Basic algebraic manipulation skills, including factoring and simplifying expressions
  • Knowledge of how to substitute trigonometric identities in expressions
NEXT STEPS
  • Study trigonometric identities in depth, focusing on their applications in simplification
  • Learn about factoring techniques in algebra to enhance expression simplification skills
  • Explore the properties of secant and cosine functions in trigonometric equations
  • Practice solving similar trigonometric expressions to reinforce understanding
USEFUL FOR

Students studying trigonometry, mathematics educators, and anyone looking to improve their skills in simplifying trigonometric expressions.

aisha
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sec theta - sec theta (sin^2 theta)

=(1/cos theta) -(1/cos theta)(sin^2 theta)

sin^2 theta = 1-cos^2 theta

so after subbing this in I got

-cos^2 theta/cos theta

so an equivalent expression would be cos theta?
 
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Looks fine to me, although where you have -cos^2 θ/cos θ, there shouldn't be a -ve sign.
 
You should have factored [itex]\frac{1}{\cos \theta}[/itex] and then it would have more clear...Yes,the final answer is [itex]\cos\theta[/itex].

Daniel.
 

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