1. Lesson 5

1.3. Explore 2

Mathematics 30-1 Module 5

Module 5: Trigonometry Applications and Identities

 

In Try This 2 you showed that it is possible to express each side of  in the equivalent form Reducing each side to a common expression is a common style of proof used for trigonometric identities. In question 5 of Try This 2, you tried to solve the equation  and probably reduced it to something like 1 = 1 or 0 = 0.

 

Although solving an identity gives a true statement, this is not a proof. Consider the equation  from the beginning of the lesson. It is also possible to simplify this to something true, but you know it is not an identity because reduces to |x + 150|, not x + 150.

 

 


caution
When proving an identity, only manipulate one side of the equation at a time. Performing an operation across the equal sign is not used when proving trigonometric identities.


textbook

Read “Example 1” on pages 310 and 311 of the textbook to see a comparison of verifying an identity and proving an identity.

 

Self-Check 1

 

Complete “Your Turn” from “Example 1” on page 311 of the textbook. Answer