 When trying to prove trigonometric identities, a very important tip to use is the following. When in doubt, convert things to sines and cosines. There's a lot of trigonometric identities out there involving the six trigonometric functions. If you could consolidate those trigonometric functions just to sine and cosine, there's a lot fewer identities and perhaps simplifications could be used to help you out there. Another potential tip that's related to this one is that cancel any common factors on the top and bottom. The idea is if we can cancel things across a fraction bar that could be very, very useful. That's where converting sines and cosines is helpful. So consider this identity. Let's prove that cosecant times tangent divided by secant is equal to one. Well, how are we gonna do that? Well, there's a secant on the bottom. There's no secants in the numerator cancel out. Not if we leave it with all of the trigonometric functions. So what we're gonna do is we're gonna take the left-hand side here. We're gonna take cosecant theta, tangent theta, divide that by secant theta. So what I'm first gonna do is I'm gonna change this fraction into a product actually. You can bring the secant up above using the reciprocal identity, in which case you're gonna end up with a cosecant theta times a tangent theta times a cosine theta. So that's one step to converting things to sines and cosines. Next, how do I convert cosecant into sines and cosines? Well, by the reciprocal, basically I put in the denominator. Cosecant is the same thing as a sine. So you get a one over sine. Tangent is the same thing as sine theta over cosine theta. And we already have a cosine in the numerator right there. Sorry, I got a little bit squished there. And so now we can see there's some cancellation going on. Notice you have a sine in the denominator, you have a sine in the numerator, they cancel out. You have a cosine in the denominator and a cosine in the numerator, they cancel out as well. What didn't cancel out are good friend number one right there. And so that finishes the proof there that cosecant times tangent divided by secant is equal to one, which was the right hand side. And therefore we've proven our trigonometric identity, that cosecant times tangent over secant is equal to one. And we did this by converting everything to sines and cosines and then simplifying. That's trigonometric identity tip number two.