I'm sure most of you have heard of trig identities involving , ,, etc...
But what about complex trigonometry? Specifically the trig function .
This function is short hand for for those of you who haven't met it before. It's used mainly to represent and calculate complex numbers.
So what happens if you add two functions together? What about subtraction, multiplication, division, how does this all affect the function?
Before we get started, I'm going to list the identities I already know which involve this function. These and all future identities will be in boxes.
Let's first expand on that second one. What if we replace with a complex number?
Knowing that really helps here.
So now that that's updated we can go on to find new identities.
We'll start with multiplication.
Alright so those are done now. Next is addition and subtraction.
And finally subtraction.
That's all for now, if there's any you think I've missed, please tell.
Edit: I forgot one:
Replace with and with
Here's the new list of identities: