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# Alternative proof for trigonometric solution? Watch

1. When , prove that .

This could be done by considering the general solution but it wouldn't really be a proof. I could do this:

So we have which will give us the required solutions.

However, is there an alternative and simpler proof for this? I ask because this question comes right after introduction to de Moivre's theorem way before hyperbolic functions.
2. (Original post by Ateo)
When , prove that .

This could be done by considering the general solution but it wouldn't really be a proof. I could do this:

So we have which will give us the required solutions.

However, is there an alternative and simpler proof for this? I ask because this question comes right after introduction to de Moivre's theorem way before hyperbolic functions.
Sorry but I fail to see why considering the general solution would not be acceptable. It is really no different to what you have done with the complex number solution.

Either or .

It doesn't get much simpler than that.

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3. You could write cos(4t)=cos(3t) as functions of cos(t) then solve that.

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Updated: April 14, 2013
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