00:01
So suppose i'm given the following expression.
00:02
I have tangent plus cotangent, all divided by cosecum.
00:07
Well, first, let's just write these as just in terms of sine and cosine.
00:10
So tangent is sine over cosine, right? co -tangent is cosine over sine, and then co -seekin is the reciprocal identity of sign.
00:24
So notice that i'm dividing two fractions.
00:25
I have my numerator fraction and my denominator fraction.
00:28
Dividing two fractions, i can multiply by the reciprocal.
00:31
Or i can multiply the entire numerator by sine.
00:39
So i can multiply by sine of x, all divided by one, and distribute this to both terms.
00:45
So what i'm going to get is sine times sine is sine squared, all divided by cosine, plus my sign cancels here, and this will just be plus cosine.
00:58
Now, what i could do, i'm going to multiply by sign at the top and bottom just for this one fraction...