00:01
Okay, so here we have to evaluate the integral of the function that are shown on the left, which is sine square of x minus cosine square of x divided by cosine of x, and we're evaluating this from negative pi over 4 to pi over 4.
00:15
So for this, we're going to apply the double angle formula in trigonometry, and rewrite it in terms of our new problem.
00:23
So for those of you who don't remember, the double angle formula is cosine square root of x minus sine squared of x is equal to two cosine squared of x minus one.
00:38
So from the integral, we have negative cosine squared x plus sine squared of x.
00:49
And all this basically is negative cosine squared x minus sine squared x minus sine squared x.
00:58
We just multiply being typing by negative 1.
01:01
And this is equal to negative 2, cosine squared x minus 1, which is equal to negative 2 cosine squared x plus 1, which is equal to 1 minus 2, cosine squared of x.
01:21
So we then plug in the simplified result back into the numerator inside the integral, and then we can simplify it further.
01:27
We can do this on the next page.
01:29
Just remember this part.
01:31
So over here, this is just 1 minus 2 cosine squared of x divided by cosine of x...