00:01
The first thing we want to do is to simplify tangent and cotangent.
00:05
The simplification of tangent is sine of x over cosine of x, while the simplification of cotangent is cosine x over sine x.
00:24
The next thing we want to do is to get our denominators the same.
00:28
So on this side, i'm multiplying top and bottom by sine x.
00:36
And on the other side, i'm multiplying top and bottom by cosine x.
00:47
This will turn out to be sine squared x over cosine x, sine x, plus cosine squared x over cosine x, sine x.
01:13
The next thing we want to do is to combine our fractions.
01:18
We're using this property, a over c plus minus b over c is equal to a plus minus b over c.
01:36
So this will look like cosine squared x plus sign squared x.
01:46
All of this over cosine x, sine x.
01:55
Now we're going to use the identity of cosine squared x plus sine squared x being equal to 1.
02:11
So this will look like 1 over cosine x, sine x.
02:24
Okay, so then now we are going to use our identity.
02:29
Another identity, cosine x, sine x, is equal to sine of 2x, multiplied by 1 over 2.
02:46
This will look like 1 over 1 half, sine of 2x...