SUMMARY
The identity \(\frac{\sin(x) + \cos(x)}{\sec(x) + \csc(x)} = \sin(x) \cos(x)\) can be proven by rewriting the left-hand side (LHS) in terms of sine and cosine functions. The LHS simplifies to \(\frac{\sin(x) + \cos(x)}{\frac{1}{\cos(x)} + \frac{1}{\sin(x)}}\). By combining the terms in the denominator, the identity can be verified step by step, leading to the conclusion that both sides are indeed equal.
PREREQUISITES
- Understanding of trigonometric identities
- Familiarity with sine and cosine functions
- Knowledge of secant and cosecant functions
- Ability to manipulate algebraic fractions
NEXT STEPS
- Study the derivation of basic trigonometric identities
- Learn how to simplify complex trigonometric expressions
- Explore the use of algebraic manipulation in trigonometry
- Practice proving other trigonometric identities
USEFUL FOR
Students of mathematics, educators teaching trigonometry, and anyone interested in mastering trigonometric identities and their proofs.