00:02
Given cosine squared x equals cosine x, we're going to algebraically determine the solutions of this equation.
00:09
To do that, we're first going to set it equal to zero, and i'm going to do this by subtracting cosine x from both sides.
00:16
We get cosine squared x minus cosine x equals zero.
00:22
We're going to let u equal cosine of x, and everywhere i see cosine x, i'm going to substitute in a u.
00:29
So i get u squared minus you equals zero.
00:33
We can now use the pythagrum theorem to solve for you, and we get you equals negative, negative one plus or minus the square root of negative one squared minus four times one times zero.
00:47
All of that over two times one.
00:51
We get you equals one plus or minus the square root of one because negative one squared is one, and then four times one times zero is just zero.
01:01
Over 2.
01:04
U equals 1 plus or minus.
01:07
The square root of 1 is 1 equals over 2...