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I'm in grade 12, and I've been given an assignment involving complex numbers.

The question reads:

Use De Moivre's Theorum to verify the identities:

[tex]cos(2\theta) = cos^2\theta - sin^2\theta[/tex]

[tex]sin(2\theta) = 2sin\theta cos\theta[/tex]

I've tried something like this:

[tex]

cos(2\theta) + i \cdot sin(2\theta) = (cos\theta + i \cdot sin\theta)^2

[/tex]

[tex]

cos(2\theta) + i \cdot sin(2\theta) = cos^2\theta + i \cdot 2cos\theta sin\theta - sin^2\theta

[/tex]

[tex]

cos(2\theta) = cos^2\theta - sin^2\theta + i \cdot 2cos\theta sin\theta - i \cdot sin(2\theta)

[/tex]

But I don't understand where to go from there. Can I somehow "separate" them?

Any help would be appreciated.

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# De Moivre's Theorum and Double-Angle Formulas

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