How to expand $2^6 \cos^7(x)$
The answer is $\cos(7x) +7\cos(5x) +21\cos(3x) +35\cos(x)$.
2026-04-25 06:56:46.1777100206
How to expand $2^6 \cos^7(x)$
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$$2\cos{(nx)}=e^{inx}+e^{-inx}$$ $$(2\cos{(x)})^7=(e^{ix}+e^{-ix})^7$$ $$=(e^{i7x}+e^{-i7x})+7(e^{i5x}+e^{-i5x})+21(e^{i3x}+e^{-i3x})+35(e^{ix}+e^{-ix})$$ $$=2\cos{(7x)}+14\cos{(5x)}+42\cos{(3x)}+70\cos{(x)}$$