Trigonometry Proving the statement is innocent

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SUMMARY

The forum discussion centers on proving the trigonometric identity (1+sinx)(1-sinx)=cos^2. Participants utilize the fundamental equation sin^2x + cos^2x = 1 to derive the proof. Key steps include recognizing the expression as a difference of squares, applying the identity (a+b)(a-b) = a^2 - b^2, and simplifying the terms correctly. The discussion highlights the importance of careful algebraic manipulation to arrive at the correct conclusion.

PREREQUISITES
  • Understanding of trigonometric identities, specifically sin^2x + cos^2x = 1
  • Familiarity with algebraic identities, particularly the difference of squares
  • Basic skills in algebraic manipulation and simplification
  • Knowledge of trigonometric functions and their properties
NEXT STEPS
  • Study the difference of squares identity in depth
  • Practice proving other trigonometric identities using fundamental equations
  • Explore advanced trigonometric identities and their applications
  • Learn about common pitfalls in algebraic manipulation in trigonometry
USEFUL FOR

Students studying trigonometry, educators teaching trigonometric identities, and anyone seeking to strengthen their algebraic manipulation skills in the context of trigonometric proofs.

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Homework Statement


Prove this statement. (1+sinx)(1-sinx)=cos^2

Homework Equations


sin^2x+cos^2x=1


The Attempt at a Solution


statement Reason
(1+sinx)(1-sinx) Given
1^2-sinx+sinx+sinx^2 GCF
1+sinx^2 Cancel
1+ (1/cscx) I'm stuck after that
 
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Hi,
Look at your negatives again, you're missing one, which is practically the final step towards finding the solution.
 
maxtheminawes said:

Homework Statement


Prove this statement. (1+sinx)(1-sinx)=cos^2

Homework Equations


sin^2x+cos^2x=1

The Attempt at a Solution


statement Reason
(1+sinx)(1-sinx) Given
1^2-sinx+sinx+sinx^2 GCF
1+sinx^2 Cancel
1+ (1/cscx) I'm stuck after that

You can simply use (a+b)(a-b) = a2 - b2, as it's considered a "commonly understood" identity.
 

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