1. Verifying a trig function means proving that the equation is true. When we do this, we can never touch the right side because it changes the original problem. It is our goal to make the left side equal the right side.
2. I have found it helpful to have all the identities (reciprocal, ratio, and Pythagorean) memorized so that it saves time. And, this allows me to recognized certain patterns and solve the equations faster. Moreover, I have found it useful to always look for a GCF because it can make an equation tremendously easier to work with.
3. When I verify a trig function, I always keep in mind what the answer is. This can give me a hint to what I need to do in order to prove it. One of the first things I always do is check if I can pull out a GCF. When applicable, this greatly simplifies the equation. Next, I check if I can change everything to sin and cos because these two trig functions are the easiest to work with and have ratio identities that may be used. Furthermore, if I see a binomial in the denominator, I try to use conjugates or LCD. If I see a binomial in the numerator, I check to see if separating the equation will help solve it. After determining the first step to take, I use the identities to further simplify the equation. I have found that after determining the first step, the rest of the equation is fairly simple. Just utilize the identities to their fullest potential and keep working even though it may look messy. Finally, always keeping the verification answer in mind can help you stay on the right track.
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