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

[abramsay]

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

 

[MHD93]

Well... I posted to here wrong.. excuse me

 

[Petr Mugver]

Try using Euler's formulas

$$\cos x=(e^{ix}+e^{-ix})/2$$

$$\sin x=(e^{ix}-e^{-ix})/2i$$

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

 

[CompuChip]

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).