00:01
So in this question, it looks like we're trying to verify an identity.
00:03
We're trying to verify that 1 minus the cosine of x over the sine of x plus the sine of x over 1 minus cosine x equals 2 cosecant x.
00:17
So to verify this, we're going to start by getting a common denominator.
00:20
My common denominator this time is sine of x times the quantity of 1 minus cosine x.
00:29
So that's going to be my common denominator.
00:34
Now in the first fraction we multiply the bottom by 1 minus cosine x.
00:40
So i've got to multiply the top by 1 minus cosine x as well.
00:47
In the second fraction i multiply the bottom by sine x so i multiply the top by sine of x as well.
00:57
And so now multiplying out we've got 1 minus 2 cosine x plus cosine squared x over sine of x times the quantity of 1 minus cosine x plus sine squared x over sine x times the quantity of 1 minus cosine x.
01:28
Now to add fractions, we add the numerators and we keep the denominator the same.
01:34
So 1 minus 2 cosine x plus cosine squared x plus sine squared x all over sine of x times the quantity of 1 minus cosine x.
01:53
Now i see a pythagorean identity...