00:01
Hi, so this problem says we have 4 sine squared x minus 4 sine x plus 1 equals 0.
00:13
So to solve for x, we kind of have to take sine x as a variable.
00:19
Let's say u equals sine x.
00:23
And then we have 4 u squared minus 4 u plus 1 equals 0.
00:32
So to solve this, we want to factor out to find what u is by itself.
00:37
So let's try and find some factors here.
00:41
Well, we know if you foil, actually reverse foil, we're going to have one and one as our numbers on the edges.
00:52
Because our one are going to multiply the equal one.
00:55
Now let me figure out which factors will sum together equal negative four.
01:00
This is a negative four, which means our sign should, probably be negative for these numbers.
01:09
We have something times negative one, something times negative one.
01:13
Something about that.
01:16
So now we have 4 u squared.
01:19
We have to factor out.
01:20
Well, we have four factors out to 2 and 2 and 1 in 4.
01:29
So let's try 2 and 2 to see if it works.
01:32
2 u, 2 u.
01:34
Now let's reverse foil to see if that works.
01:38
We have 2 u times 2 u, which is 4 u squared then we have 2 u times negative 1 and negative 1 times 2 u so we get negative 2 u negative 2 u and finally we get negative 1 times negative 1 which means our answer should be 4 u squared minus 4 u plus 1 which is what we wanted and so our foil is 2u minus 1 times 2 u minus 1 equals 0.
02:28
Now we want to substitute our, actually we don't substitute you back in just yet, but we can solve for u by itself...