1. What does it actually mean to verify a trig identity?
To verify a trig identity is to be given a an equation and solve the problem so that the left side of the problem eventually equals to the right side of the equal sign. This means that the right side of the equal sign will not be messed with, or touched, at all. The point of verifying a trig identity is to "verify" that the problem actually amounts to the given answer.
2. What tips and tricks have you found helpful?
I found knowing/memorizing the identities extremely helpful because they're necessary for substituting into trig functions in order to isolate what I want. Another important tip is to convert everything to sin and cosine because it just makes everything easier to work with.
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 verifying a trig function, I make sure I never touch the right side of the equal sign. I try to see if I can convert anything to fit into the trig function(s) on the other side. The identities are extremely important for doing this. Complex problems with various trig identities within them have to be taken apart piece by piece in order to reduce the work and make it simpler.
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