1.) What does it actually mean to verify a trig identity?
To verify a trig identity means to simplify an expression with trig functions until it equals something. When someone asks you to 'verify a trig identity', they mean 'look, here's two expressions that are set equal to each other. Make one side look like the other side.' Usually this consists of simplifying the more complex side to that it has the same terms as the simpler side. It also usually involves substituting trig identities to get things to cancel (and therefore simplify.)
2.) What tips and tricks have you found helpful?
I personally like to convert everything to sine and cosine. It makes it easier for me to see what cancels and what can be substituted (particularly with the Pythagorean Identities.) I also find it helpful to use the Reciprocal Identities to convert everything to the same trig function. Again, it makes it easier for me to see what cancels. Another tip is to try to get things to cancel to 1 (when there's multiplication or division) or 0 (when there's addition or subtraction.)
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.
Like I explained in the second answer, I like to try to use the Reciprocal Identities to cancel things out. I don't like to convert everything to sine and cosine until later on in the solving process. This is because converting to sine and cosine too early in the solving process can make things needlessly complicated. My last resorts are squaring the expression or multiplying by a conjugate (because those are almost guaranteed to make things very complicated.)
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