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