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Euler's formula states that eθi=cosθ+i*sinθ. We can square both sides to get e2θi=cos2θ-sin2θ+i*2sinθcosθ. But we also know that e2θi=cos(2θ)+i*sin(2θ) (by applying Euler's formula to 2θ). Matching up the real and complex parts, we get the double angle formulas: cos(2θ)=cos2θ-sin2θ sin(2θ)=2sinθcosθ

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Q: How do you use Euler's formula to verify the cos double angle formulas?
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