00:01
So i have this identity and i wish to verify it.
00:03
I'm going to work on the left -hand side and i'm going to multiply both the numerator and the denominator by sine x minus x minus 1.
00:21
And on the numerator that is going to multiply out to give me sine squared x minus 2 plus x sine x plus squared x minus 1 and on the denominator that is going to multiply out to give me sine squared x minus 2 sine x minus cos squared x plus 1.
01:02
Just remembering the old formulae for multiplying out special brackets.
01:11
And from this we can further simplify.
01:16
If we have a look at the numerator, we have cos squared x and we have sign squared x.
01:20
And we know the identity, sine squared x plus cosquod x equals 1.
01:25
And we also have minus 1, so that's going to cancel out.
01:30
To just give us minus 2, cos x, sine x, on the numerator.
01:40
And on the denominator, we have sine square x minus 2, sine x, minus cos squared x plus 1.
01:47
I'm going to take this and look at the density sine square x plus cos square x equals 1, which makes 1 minus cos square x sine square x...