Proving an identity does not follow a set pattern; each proof is unique. Here are some strategies that may be useful.
The most important suggestion of all is DON’T GIVE UP. You will rarely write a proof correctly on your first try. Proving an identity will often require multiple attempts, a lot of scrap paper, and a bit of luck—none of which are shown in examples of proofs. Be patient.
Complete Try This 3 with a group if possible, but alone if necessary.
Consider the identity csc x(1 + sin x) = 1 + csc x.
How many different proofs are possible? Explain.
How do you know when you are finished a proof?
Save your responses in your course folder.
Compare your proof to the proofs of other students. Your comparisons can include considerations like length, difficulty, clarity, and the strategy used.
If required, save your responses and a record of your discussion in your course folder.
Review the list of strategies provided just before Try This 3.