00:01
Okay, so what does it mean to verify an identity? well, looking at my left side and my right side of my equation, what i could do is pick one side of an equation, transform it using different trick identities, pythagorean identities, reciprocal identities, even odd identities, so on and so forth, to eventually get to my other side.
00:18
Because if one side equals another side, one equals one, this will be always true.
00:22
So i'm going to pick my left side.
00:24
I see that i'm adding two fractions, so i'm going to multiply by the denominator of the other first.
00:30
Fraction to each term so that, and i have to do this to the bottom and top, which is the same as multiplying by one to each term.
00:40
In my numerator, i'm going to get 1 plus cosine of x plus 1 minus cosine of x.
00:46
I can see easily that cosine and cosine will cancel.
00:50
Now i'm multiplying 1 plus cosine times 1 minus cosine, multiply my first term, 1 times 1 is 1, 1 times cosine of x is cosine of x, negative cosine of x times 1 is negative cosine of x.
01:04
Negative cosine of x times positive is negative cosine squared of x.
01:09
Cosin in the middle cancels...