Statement-1: $\cos^{3} α + \cos^{3} (α + \frac{2 π}{3}) + \cos^{3} (α + \frac{4 π}{3}) = 3 \cos α \cos (α + \frac{2 π}{3}) \cos (α + \frac{4 π}{3})$
Statement-2: If $a + b + c = 0 \Leftrightarrow a^{3} + b^{3} + c^{3} = 3 a b c$

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If both Statements are TRUE and Statement-2 is the correct explanation of Statement-1

If Statement-1 is TRUE and Statement-2 is FALSE

If both Statements are TRUE and Statement-2 is NOT the correct explanation of Statement-1

If Statement-1 is FALSE and Statement-2 is TRUE

answer is A.

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Detailed Solution

$∵ \cos α + \cos (α + \frac{2 π}{3}) + \cos (α + \frac{4 π}{3})$
$= \cos α + 2 \cos (π + α) . \cos \frac{π}{3} = \cos α - 2 \cos α . \frac{1}{2} = 0$
$∴$ we know that, $a^{3} + b^{3} + c^{3} = 3 a b c$
if $a + b + c = 0$
$∴ \cos^{3} α + \cos^{3} (α + \frac{2 π}{3}) + \cos^{3} (α + \frac{4 π}{3}) = 3 \cos α \cos (α + \frac{2 π}{3}) \cos (α + \frac{4 π}{3})$