- So if you guys see something you can apply operations, then apply operations. Now, again, one of the big mistakes that I still see people doing is writing this as sine squared of theta plus cosine squared of theta. This squared does not equal that. This squared means sine of theta plus cosine of theta times sine of theta plus cosine of theta. It's a binomial squared. 

Remember we did binomial expansion? Remember like Pascal's triangle? It doesn't equal that. Anyways, and if it did equal that, that would equal 1. And obviously, is this an identity then? No. So you'd know you did something wrong. 

Now, we can apply FOIL here, which I'm not going to go through these steps. So once you apply FOIL, you'll get sine squared of theta plus a 2 cosine of theta sine of theta plus a cosine squared of theta. Now, you guys recognize here? Now we have this Pythagorean relationship which is a sine squared of theta plus cosine squared of theta, which we know is 1 plus a 2 cosine of theta sine of theta. 

Now, again, we want this to equal 1 plus sine of 2 theta. So we have the 1. And then we recognize this. This is actually our double angle formula. There you go. Easy, breezy, beautiful CoverGirl.