1. What does it mean to verify a trig identity?
To me, verifying an identity basically means to prove that an equation is true by showing that both sides are equal. I think of it as taking steps to simplify one side of the equation to make it equal to the other. Verifying a trig identity takes a gradual process of manipulation, alterations, and logical thinking! It may be difficult at first, but all you have to do is to make both sides equal and there are multiple steps so it is not as difficult as other math units.
2. What tips and tricks have you found helpful?
I found that remembering the identities (ratio, reciprocal, Pythagorean) make verifying a trig identity much faster. Also, I learned that it's a little different than other units we have went through, because there are many ways to verify an identity and it's very ambiguous. Usually, we are usually used to using a formula and getting our answer right away, but with this we basically we have trial and error. Another tip is to not touch the other side! You simply cannot, no matter how tempting it is.
3. Explain your thought process and steps you take in verifying a trig identity.
First, I look at the problem and I try to convert anything to a trig identity of sine or cosine. Next, I usually look to see if I can take out a LCD (least common denominator). I factor if I need it. Then, I usually check if I can use any identities, especially Pythagorean identities. I also find that powering up can lead me to the Pythagorean identity. I sometimes multiply by conjugate if there is any fraction. If I get confused at all, I usually go to three steps back and review what I did. If I can't make sense of it, I usually start from scratch because I don't want to over complicate the equation and continue if I accidentally made an error.