Basic properties and formulas of algebra, such as the difference of squares formula and the perfect squares formula, will simplify the work involved with trigonometric expressions and equations. In fact, we use algebraic techniques constantly to simplify trigonometric expressions. They are the basic tools of trigonometry used in solving trigonometric equations, just as factoring, finding common denominators, and using special formulas are the basic tools of solving algebraic equations. Identities enable us to simplify complicated expressions. Verifying the Fundamental Trigonometric Identities In this section, we will begin an examination of the fundamental trigonometric identities, including how we can verify them and how we can use them to simplify trigonometric expressions. Just as a spy will choose an Italian passport when traveling to Italy, we choose the identity that applies to the given scenario when solving a trigonometric equation. The trigonometric identities act in a similar manner to multiple passports-there are many ways to represent the same trigonometric expression. However, we know that each of those passports represents the same person. In espionage movies, we see international spies with multiple passports, each claiming a different identity. Figure 1 International passports and travel documents
