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I was working with a student today, and as we worked through the section in his book dealing with Trigonometric Identities and Pythagorean Identities, we stumbled across a problem that gave us a bit of trouble. The solution is not so complicated, but it sure had us stumped earlier.   The problem was presented as such:       Factor and simplify the following using Trigonometric and Pythagorean Identities:   sec3(x) - sec2(x) - sec(x) + 1       We tried a couple of different approaches, such as factoring sec(x) from each term:   sec(x) * [ sec2(x) - sec(x) - 1 + 1/sec(x) ]   and factoring sec2(x) from each term:   sec2(x) * [ sec(x) - 1 - 1/sec(x) + 1/sec2(x) ]   We followed these approaches through a few steps, but nothing we were attempting led to the solution. After doing some reading online, I found that the solution required a simple... read more