00:01
For this problem, we are asked to find the mclauran series for the function f of x equals cos squared of x.
00:05
Where i'll note, well, that is the same thing as cos of x times cos of x, which we can then write out using the series, the known series expansion for cos of x.
00:16
It would be 1 minus x squared over 2 factorial, plus x power of 4 over 4 factorial, minus x power of 6 over 6 factorial, plus x power of 8 over 8 factorial, times that exact same thing.
00:30
So i'm just going to use my magical powers here.
00:33
Copy and paste that over.
00:37
And we can figure out how that multiplies out by writing this.
00:41
I'm going to copy and paste this again.
00:49
So we then have plus dot dot dot.
00:51
And we want to be multiplying by first...