Cos(nt) = 3sin(2nt) + cos(2nt)

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abramsay
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Picked up a question and decided to try my hands on it.

I got to this point where I'm to find 't' and I got stuck. Anyone wants to help?

cos(nt) = 3sin(2nt) + cos(2nt)
where n is a constant.

I tried making nt=x and use double angles but still not getting through.

Thanks
 

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Well... I posted to here wrong.. excuse me
 
Last edited:


Try using Euler's formulas

[tex]\cos x=(e^{ix}+e^{-ix})/2[/tex]

[tex]\sin x=(e^{ix}-e^{-ix})/2i[/tex]

Your equation will become a second order polynomial in [tex]e^{int}[/tex] which should be easy to solve.
 


I have also found a slightly more elaborate way, which I will post if you're interested (Petr's idea is probably more useful though).