(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

So im a little rusty on my basic math and I am trying to simplify this expression. In case you were curious the expression came from a signal block diagram that I calculated the transfer function H(z) to then found the frequency response H(f) and I think i have done that correctly I just need to reduce this further. I have attached a picture of what I have left. The theta stands for exp(j2pifT) if that maters to you.

2. Relevant equations

3. The attempt at a solution

So this is where I get confused and cant remember the proper rules. These are super basic I know. Unfortunately I never learned them that well to begin with which is why im having trouble now..

the terms that are j*sin(-2*theta) can I bring the -2 out of the sin function? Same with the cosine? I want to say no but part of me feels like you can..... If so im thinking this might help me cross out a few terms?

Or if i break it up into sections i get something like this for the first few terms. -2/4 * cos(-theta)/cos(-theta). I then feel like i can cross out the cosine terms and be left with -1/2? Same with the -2jsin(theta)/4jsin(theta) etc.

Am I going about this correctly? Some of it just doesn't seem right to me.

I really appreciate any help here guys/girls.

Thanks

p.s. Sorry if my handwriting is messy. I tried my best to write it down as neat as possible. I figured it would be easier to see if i took a picture rather then type it out here and have you try to understand what im looking at.

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# Homework Help: Simplifying cosine and sine expressions

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