The general solution of the equation 8cos x cos2x cos4x = sin6x / sin x is

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$x = (nπ / 7) + (π / 14), \forall n \in Z$

$x = (2 nπ / 7) + (3 π / 14), \forall n \in Z$

$x = (3 nπ / 7) + (5 π / 14), \forall n \in Z$

$x = (5 nπ / 7) + (3 π / 14), \forall n \in Z$

answer is A.

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Detailed Solution

The given equation is
8sin x cos x cos2x cos 4x = sin 6x(sin x $\neq$ 0)
$\Rightarrow \sin 8 x = \sin 6 x \Rightarrow 2 \cos 7 xsin x = 0,$
i.e., $x = nπ / 7 + π / 14; n \in Z$

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