SUMMARY
The expression 2cos2x - 2cosx simplifies to 2(cos2x - cosx). To solve the equation 2cos(2x) - 2cos(x) = 0, one must find x such that cos(2x) = cos(x). Utilizing the identity cos(2x) = 2cos²(x) - 1 leads to the equation 2cos²(x) - cos(x) - 1 = 0. Factoring this results in (2cos(x) + 1)(cos(x) - 1) = 0, providing the solutions for x.
PREREQUISITES
- Understanding of trigonometric identities, specifically cos(2x) = 2cos²(x) - 1
- Ability to solve quadratic equations
- Knowledge of periodic functions in trigonometry
- Familiarity with factoring polynomials
NEXT STEPS
- Study the unit circle to understand the periodic nature of cosine functions
- Learn how to derive and apply trigonometric identities
- Practice solving quadratic equations in trigonometric contexts
- Explore graphical methods for solving trigonometric equations
USEFUL FOR
Students studying trigonometry, educators teaching trigonometric identities, and anyone looking to deepen their understanding of solving trigonometric equations.