Proving trig functions isn't nearly as difficult as you might be assuming, so long as you break everything down into a series of manageable steps. Learn about proving trig functions with help from a longtime mathematics educator in this free video clip.
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Hi, I'm Jimmy Chang, and we're here to talk about proving trig functions. Now when you're proving trigonometric functions often times you're going to end up using a few things such as Pythagorean identities or actually any kind of identities or definitions that go along with the trig functions. So depending on what it is that you're asked to prove there's a couple of things to consider. As we talked about just now, one of the things you might want to consider is the use of Pythagorean identities to help prove trig functions. Now, here's just a couple of them to consider. One of the ones that you'll find quite a bit of is sine square theta plus cosine square theta is equal to 1. That's probably one of the more frequently used Pythagorean identities. Now there's a couple of other ones such as 1 plus tangent squared theta of the angle which is equal to secant squared theta of the angle which is equal to secant squared theta as well as one plus cotangent squared theta is equal to cosecant squared theta. Now in addition to these identities you may be asked to use some reciprocal functions for example, you may be, when it comes to proving trig functions you may be asked to use the fact that secant theta is equal to 1 over cosine theta or cosecant theta is equal to 1 over sine theta. Now these are just a couple of different demonstrations but you might ask to use what sine and cosine are in terms or reciprocals so for example, cosine theta you might be asked to use the fact that it's 1 over secant theta and similarly that sine theta is 1 over cosine secant theta. So depending on what it is that you're trying to prove you may be asked to use various Pythagorean identities or reciprocal definitions. So I'm Jimmy Chang and there are a few tips on proving trig functions.