Solving the Equation: (sinθ + cosθ)2 = 1 + 2sinθ cosθ

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SUMMARY

The equation (sinθ + cosθ)² = 1 + 2sinθ cosθ is a mathematical identity that can be verified by expanding the left side using the binomial theorem. The expansion results in sin²θ + 2sinθ cosθ + cos²θ, which simplifies to 1 + 2sinθ cosθ, confirming the identity. This discussion emphasizes the importance of recognizing and applying algebraic identities in trigonometry.

PREREQUISITES
  • Understanding of trigonometric identities
  • Familiarity with the binomial theorem
  • Basic algebraic manipulation skills
  • Knowledge of sine and cosine functions
NEXT STEPS
  • Study the binomial theorem and its applications in algebra
  • Explore more trigonometric identities and their proofs
  • Practice expanding binomial expressions in various contexts
  • Learn about the unit circle and its relationship to sine and cosine functions
USEFUL FOR

Students studying trigonometry, educators teaching algebraic identities, and anyone looking to strengthen their understanding of mathematical proofs and manipulations.

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Homework Statement


(sinθ + cosθ)2 = 1 + 2sinθ cosθ

Homework Equations

The Attempt at a Solution


Would I have to foil out the left side?
 
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Veronica_Oles said:

Homework Statement


(sinθ + cosθ)2 = 1 + 2sinθ cosθ

Homework Equations

The Attempt at a Solution


Would I have to foil out the left side?
Why don't you try it? After all, you should be able to expand the square of a binomial expression rather easily.
 

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