1. What does it actually mean to verify a trig identity?
Verifying a trig function means to prove that one side is equal to the other side, to prove that it is true. This can be accomplished through manipulating one side of the equation to make it look like what we want it to. This is usually making the left side look like the right side of the equations. To verify, identities are used to simplify the equation as much as possible in order to get to the point we want them to be.
2. What tips and tricks have you found helpful?
Since there are no set steps to verifying trig functions, it can be a bit confusing, like a puzzle. However, the biggest tip I have, is to practice, practice, practice! This is a concept that takes a lot of practice problems in order to improve. Practice is very beneficial in the fact that it helps you memorize the identities as well as recognize patterns. Depending on how the problem is formatted, different approaches need to be taken. Although there are no set ways to approach a problem, there are indeed patterns that are useful when recognized.
3.Explain your thought process and steps you take in verifying a trig identity. Do not use a specific example, but speak in general terms of what you would do no matter what they give you.
When I first begin verifying a trig functions, I check to see if I have solved a similar problem before hand. If it is entirely new, there are a couple approaches that I find useful. When I am stuck, I find it helpful to
look for the greatest common denominator. If there is none, I check to see if I can substitute for and identify or if changing everything to sin and cos. If this is not possible, I check if
multiplying a conjugate will be helpful. If all these are not useful, I use various other simplification
methods that include combining fractions with a binomial denominator,
separating fractions with monomial denominators, or factoring.