Precalculus 5.1 pg 1You need to be able to work with identities and establish equivalencies.You can show an identity to be true by working with one side only and transforming it into the other sideor working with both sides and find a common statement.There is no substitute for experience when it comes to verifying identities. You just need to practice withthem. All the examples I will do will be true identities. On your homework and quizzes they may or may not be true. If they are true, then you will need to select the “Identity” choice. If the identity is not true (not equivalent), then you will need to select the choice “Not an identity”.Working with one side1)Verify cotxsinx sec x=1cotxsinx sec x=1page 207
Precalculus 5.1 pg 2Substitute, using the fundamental identities, equivalencies for cot x and sec x. This changes the statement into sines and cosines only.cosxsinx∙sinx∙1cosx=¿The sine statements reduce to 1 and the cosine statements reduce to 1, therefore, the left side is 1 which is equivalent to the right side.1=1We have shown the identity to be true.2)Verify cot2θ(tan2θ+1)=csc2θSometimes there is only one way to proceed to show the identity to be true. Other times, like this problem, there is more than one way to show the identity to be true. Let me show you both ways.