SUMMARY
The inequality (1 + tg(x)) * cos^2(x) > 1 can be solved by transforming it into the form sin(x)cos(x) > sin^2(x). The key steps involve using the identity tg(x) = sin(x)/cos(x) and the double angle identity sin(2x) = 2sin(x)cos(x). The final rearrangement simplifies the problem, making it easier to solve without needing the quadratic formula.
PREREQUISITES
- Understanding of trigonometric functions, specifically tangent and cosine.
- Familiarity with trigonometric identities, including double angle identities.
- Ability to manipulate inequalities involving trigonometric expressions.
- Knowledge of basic algebraic rearrangement techniques.
NEXT STEPS
- Study the derivation and application of trigonometric identities, particularly double angle identities.
- Learn how to solve trigonometric inequalities effectively.
- Explore the implications of rearranging trigonometric expressions in inequalities.
- Practice solving similar inequalities involving trigonometric functions.
USEFUL FOR
Students studying trigonometry, educators teaching trigonometric inequalities, and anyone looking to enhance their problem-solving skills in mathematics.