1. When a problem asks you to "verify a trig identity", it basically means to work out one side of the equation, simplifying it to the point to where it equals the other side. It is almost as if the problem gave you the starting and ending points and you are just finding the steps to get from one to the other.
2. First of all, make sure you memorize all the identities. They're honestly not that difficult to remember after dealing with them SO MUCH, and it is a nice thing to know that this equals this at the top of your head. However, sometimes just knowing these identities, does not do anyone any good. I find changing everything in terms of cosine and sine makes everything a lot easier. What I like to say is "When in doubt, do sine and cosine." and it's pretty much true. Also, u substitution was such a blessing on my mind. It basically allows us to replace a trig function with "u" when we have a quadratic on our hand. Trust me, you do not want to be "x-boxing" or factoring or FOILing (sinx +1)^2. I don't know if these can actually be called "tricks" that helped me get through this unit, but I know these reminders saved my life on the test. For verifying, it is essential for you to know that touching the "right side" (the side that you're usually trying to work towards), is a BIG NO NO. Another thing I found helpful was knowing that whenever you square anything, you are going to end up with extraneous solutions; as a result, you will need to make sure you actually plug your answers into the original equation to ensure the "correctness" (is that a word...?) of the answer.
3. Whenever I see a problem that asks to verify, I get excited because they practically told you what you're supposed to end up with! Now you just have to find your way to the end. My general thought process is, "Are there any trig functions that can convert to sine and cosine?". If I see cotangent or cosecant, and so on (you get the point), I would usually replace them with sine and cosine. However, sometimes that does not work for me, so my next thought is "Are there any trig functions that are squared?" Usually, if something is squared, I would replace that with a Pythgagorean Identity, and then go from there. If I see that I have a binomial as my denominator, I will multiply the entire fraction by the conjugate. If I see two/ multiple fractions being added together, I will make sure the two have the same denominator, and if they don't (which is 90% sadly), then I would have the lowest common denominator (LCD) between the two, multiply each fraction with what is needed to achieve that LCD, and then combine them so I have one large fraction. Again, I really only focus on the left because we don't really need to do anything to the right. This is just really what I think in general, and my thinking will change depending on the types of problems I am given. Ultimately, the best piece of advice I could give to you when dealing with verifying is just to go through it slowly and rationally. Don't feel the need to rush and you'll be able to get through these like nothing.
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