lunnatican4

2021-12-17

What's the formula for ${\mathrm{cos}}^{3}A$?

Linda Birchfield

Expert

${\mathrm{cos}}^{3}A$
$=\mathrm{cos}\left(A+2A\right)$
$=\mathrm{cos}\left(A\right)\mathrm{cos}\left(2A\right)-\mathrm{sin}\left(A\right)\mathrm{sin}\left(2A\right)$
$=\mathrm{cos}\left(A\right)\left(2{\mathrm{cos}}^{2}\left(A\right)-1\right)-\mathrm{sin}\left(A\right)\left(2\mathrm{sin}\left(A\right)\mathrm{cos}\left(A\right)\right)$
$=2{\mathrm{cos}}^{3}\left(A\right)-\mathrm{cos}\left(A\right)-2{\mathrm{sin}}^{2}\left(A\right)\mathrm{cos}\left(A\right)$
$=2{\mathrm{cos}}^{3}\left(A\right)-\mathrm{cos}\left(A\right)-2\left(1-{\mathrm{cos}}^{2}\left(A\right)\right)×\mathrm{cos}\left(A\right)$
$=2{\mathrm{cos}}^{3}\left(A\right)-\mathrm{cos}\left(A\right)-2\left(\mathrm{cos}\left(A\right)-{\mathrm{cos}}^{3}\left(A\right)\right)$
$={\mathrm{cos}}^{3}\left(A\right)-\mathrm{cos}\left(A\right)-2\mathrm{cos}\left(A\right)+{\mathrm{cos}}^{3}\left(A\right)$
$=4{\mathrm{cos}}^{3}\left(A\right)-\mathrm{cos}\left(A\right)-2\mathrm{cos}\left(A\right)$
$=4{\mathrm{cos}}^{3}\left(A\right)-3\mathrm{cos}\left(A\right)$

Bukvald5z

Expert

${\mathrm{cos}}^{3}\left(A\right)=4{\mathrm{cos}}^{3}\left(A\right)-3\mathrm{cos}\left(A\right)$

RizerMix

Expert

The formula for

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