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 $a + b + c = 0 \Leftrightarrow a^{3} + b^{3} + c^{3} = 3 a b c$

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

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.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

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 $a + b + c = 0$
$∴ \cos^{3} α + \cos^{3} (α + \frac{2 π}{3}) + \cos^{3} (α + \frac{4 π}{3}) = 3 \cos α \cos (α + \frac{2 π}{3}) \cos (α + \frac{4 π}{3})$