$4 (\cos^{3} 20 ° + \cos^{3} 40 °) =$

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$3 (\cos 20 ° + \cos 40 °)$

$3 (\sin 20 ° + \sin 40 °)$

$3 (\cos 20 ° - \cos 40 °)$

$3 (\sin 20 ° - \sin 40 °)$

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Detailed Solution

$4 (\cos^{3} 20 ° + \cos^{3} 40 °)$

$\cos 3 (20 °) = 4 \cos^{3} 20 ° - 3 \cos 20 °$

$\cos 3 (40 °) = 4 \cos^{3} 40 ° - 3 \cos 40 °$

$4 (\cos^{3} 20 ° + \cos^{3} 40 °) = \cos 60 ° + 3 \cos 20 ° + \cos 120 ° + 3 \cos 40 °$

$4 (\cos^{3} 20 ° + \cos^{3} 40 °)$ $= \frac{1}{2} + 3 \cos 20 ° + 3 \cos 40 ° - \frac{1}{2}$

$4 (\cos^{3} 20 ° + \cos^{3} 40 °)$ $= 3 \cos 20 ° + 3 \cos 40 °$

$4 (\cos^{3} 20 ° + \cos^{3} 40 °)$ $= 3 (\cos 20 ° + \cos 40 °)$

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