00:01
So i'm going to start with the left -hand side because it's a lot more complex than the right.
00:07
So we have cosine x over 1 plus sine plus cosine x over 1 minus sine x.
00:24
So now, because we have two different denominators and we want to have a common denominator, we're going to multiply the other fraction by the other denominator.
00:33
So like for the first one, we're going to multiply by 1 minus sine x because that's the denominator of the other fraction.
00:43
And for the second one, we're going to multiply by 1 plus sine x over 1 plus sine x.
00:53
So now we have this common denominator of 1 minus sine x times 1 plus sine x.
01:09
So on top we'll have cosine x times 1 minus sine x plus cosine x plus cosine x plus cosine.
01:20
X times 1 plus sine x so now we're going to simplify this bottom so i'm going to leave the top the same cosine x times 1 minus sine x plus cosine x times 1 plus sine x and we're going to multiply out the bottom or foil so you do first 1 times 1 outer plus sine x oh, it's a difference of squares.
02:06
So it's automatically 1 minus sine squared x.
02:13
And now we're going to replace the bottom and have, i don't know how to keep the numerator.
02:35
So this bottom, if you can recall the pythagorean identity, that sine squared x plus cosine square x equals 1.
02:44
We can redefine it by subtracting sign from both sides...