Derive the Triple Angle Formula Complex Analysis

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We can use the de Moivre's formula:

$$e^{i3\phi}=\cos3\phi+i\sin3\phi=(\cos\phi+i\sin\phi)^3=\cos^3\phi-i\sin^3\phi+3i\cos^2\phi\sin\phi-3\sin^2\phi\cos\phi$$

Identifying real and imaginary parts: $$\cos3\phi=\cos^3\phi-3\sin^2\phi\cos\phi$$ $$\sin3\phi=3\cos^2\phi\sin\phi-\sin^3\phi$$

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HrmMz
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HrmMz

Updated on July 23, 2022

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  • HrmMz
    HrmMz over 1 year

    Derive the Triple Angle Formula using the stated proposition:

    Details to Derive Triple Angle Formulas

  • HrmMz
    HrmMz almost 7 years
    Thanks, I had just done a general proof that didn't use de moivre's formula..