1. What does it mean to verify a trig identity?
To verify a trig identity just means that you are just verifying, or proving, that the equation is true. That means you have to use logical steps to show that one side of the equation equals another. However, you can only work on one side of the identity at a time.
2. What tips and tricks have you found helpful?
You should probably be knowledgeable in all the identities. If you knew all your ratio, reciprocal, and Pythagorean identities, then it would be quicker and easier for you to verify. Pythagorean identities could especially be helpful when you have a squared trigonometric function. There are several ways to verify a trig identity, so a different combinations of techniques would still get you the same answer. You should start off with the more complicated side first. You look for a GCF (greatest common factor), LCD(least common denominator), multiply by the conjugate, factor, or substitute an identity. If you have a monomial denominator, then you could separate the fractions or if you have a binomial denominator, you can try combining the fraction. As a last resort, you can convert everything to sine and cosine.
3. Explain your thought process and steps you take in verifying a trig identity.
I always first look if the identity could have a GCF that I could factor out or FOIL. If not, I look to see if substituting an identity would help me. Like if a function is squared, then I'll check if I can use a Pythagorean Identity. If the identity is a fraction, I'll check to see if I'll either multiply the conjugate, separate it into fractions if it has a monomial denominator, combine other fractions with a binomial denominator with a LCD. If nothing else works, I would just convert everything to sine and cosine and try to cancel everything out so that it is equal to the other side.
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