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Complex Numbers! (1 Viewer)

harshsyd

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Hey, I got two questions;

I'll attach the images as I cannot use LaTeX for some reason.

1. https://imgur.com/a/CFbQErW (I tried expanding and simplifying using bionomial, I do get correct answers but of course they are not in the forms of cot and so on, I get straight square roots, expected).

2. https://imgur.com/a/eF2Su32 (The only real place I am struggling is the last part, deducing the cos(2O) statement, rest is completed).

Thank You! :)
 

harshsyd

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Thank you buddy, that was very nicely explained!
Except, how was the second last line derived? I understood up till 1+cosO+isinO/1-cosO-isinO...the half angles one, I am slightly lost
 
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fan96

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I think the start of that second last line you were talking about should read:

 

fan96

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For your second question:

Let .



Note:


Similarly,


Going back to the original identity: multiplying the expression on the RHS and taking the real part of both sides,



And a few more lines of working give the required identity.
 

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