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Smallest positive ‘x’ satisfying the equation $\cos^{3} 3 x + \cos^{3} 5 x = 8 \cos^{3} 4 x \cdot \cos^{3} x$ is

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22.5°

30°

15°

18°

answer is B.

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Detailed Solution

$\cos^{3} 3 x + \cos^{3} 5 x = {(2 \cos 4 x \cdot \cos x)}^{3}$

$\cos^{3} 3 x + \cos^{3} 5 x = {(\cos 5 x + \cos 3 x)}^{3}$

$\Rightarrow 3 \cos 5 x \cdot \cos 3 x (\cos 5 x + \cos 3 x) = 0$

Let $n = 0, x = \frac{π}{10} = \frac{180}{10} = 18 °$

The least value of ‘x’ is $18 °$

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