 Another tip for proving trigonometric identities is the following. When adding or subtracting trigonometric functions, always find a common denominator. If you're not sure how to add or subtract things, write them as fractions and then have a common denominator. Believe it or not, that simplification, that idea of using fractions can actually be useful for us. So in this situation, let's prove the identity sine theta plus cosine theta times cotangent is equal to cosecant. Starting with the left-hand side, we have sine theta plus cosine theta, cotangent theta. So not sure what to do. I might use one of my previous tips of writing everything in terms of sine and cosine. Sine, of course, is already in that regard, so it's cosine. But cotangent, I can write as cosine over sine, for which when you multiply together the cosine with the fraction there, you're gonna end up with sine theta plus cosine squared over sine. So in the process of writing cotangent as cosine over sine, I introduce fractions into the problem. Well, how am I gonna add those together? Well, if I could have a common denominator, that would be very helpful. I would want a sine in the denominator, but if you're gonna put a sine in the denominator, you have to put another sine in the numerator, which I can live with that, right? For which then we get sine times sine, which is a sine squared plus a cosine squared, and this all sits above sine. Now I see there are squares now involved in my identity. I have a sine squared and a cosine squared. So my Pythagorean sense is tingling right now. Whenever squares are involved, you probably are gonna use a Pythagorean identity. In fact, we're gonna use the mother of all identities that is cosine squared plus sine squared is equal to one. And so since I have a sine squared plus cosine squared, that becomes a one in the numerator, one over sine. And then there you go, one over sine, that's the same thing by reciprocation. That's just cosecant, which is the right-hand side. And so we've now proven our identity. So like we saw here, that if you have to add together fractions or subtract fractions, well, you're gonna need to find a common denominator. So rescale things so that you have a common denominator, add them together, and perhaps that's the trick you need. And so this gives us proving trigometric identity tip number four.