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**ronaldo_07** Using Euler’s formula, express in terms of $\displaystyle sin\alpha$ and $\displaystyle cos\alpha$ for :

$\displaystyle sin2\alpha$ and $\displaystyle cos2\alpha$

I know that Euler's formula is :

$\displaystyle e^{ix}$ = $\displaystyle cos\alpha$ + $\displaystyle isin\alpha$

So I have come to the conclusion that:

$\displaystyle cos2\alpha =Re[e^{2i\alpha}]$ and $\displaystyle sin2\alpha =Im[e^{2i\alpha}]$

Is this correct and to answer this question do I leave it in this form?