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.