Trigonometric Equation Simplification Strategies

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SUMMARY

The discussion focuses on simplifying the trigonometric expression (sec² x - 1)/(sin² x) to arrive at the conclusion that the answer is sec² x. Participants emphasize the use of trigonometric identities, particularly the relationship sec² x = 1/cos² x and the identity 1 - cos² x = sin² x, to facilitate the simplification process. The step-by-step breakdown provided illustrates how to manipulate the expression effectively using these identities.

PREREQUISITES
  • Understanding of trigonometric identities, specifically secant and sine functions.
  • Familiarity with algebraic manipulation of fractions.
  • Knowledge of the Pythagorean identity: 1 - cos² x = sin² x.
  • Basic skills in simplifying rational expressions.
NEXT STEPS
  • Study the derivation and applications of the Pythagorean identities in trigonometry.
  • Learn how to manipulate and simplify trigonometric expressions using algebraic techniques.
  • Explore the properties and graphs of secant and sine functions for better visualization.
  • Practice solving various trigonometric equations to reinforce understanding of identities.
USEFUL FOR

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

parise19
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Homework Statement



(sec^2 x - 1)/(sin^2 x)

Homework Equations





The Attempt at a Solution



i know that the answer is sec^2 x, but i have no idea what steps to take to get there
 
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What trig identities do you know? There are several that would be helpful here.
 
Do you know what sec2x equals to?

secx=1/cosx

Can you try to solve it for your own?

I will help you little bit.

[tex]\frac{\frac{1}{cos^2x} - 1}{sin^2x}=\frac{\frac{1-cos^2x}{cos^2x}}{sin^2x}[/tex]

Do you know what 1-cos2 equals to?

Regards.
 

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