First slide

Trigonometric equations

Question

The general solution of the equation $8 \cos xcos 2 xcos 4 x = \sin 6 x / \sin x$ is

Moderate

A

$x = (nπ / 7) + (π / 21), \forall n \in Z$
B

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

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

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

Solution

The given equation is
$\begin{array}{l} 8 \sin xcos xcos 2 xcos 4 x = \sin 6 x (\sin x \neq 0) \\ \Rightarrow \sin 8 x = \sin 6 x \\ \Rightarrow 2 \cos 7 xsin x = 0 \\ As \sin x \neq 0, \cos 7 x = 0 \\ or 7 x = nπ + π / 2, n \in Z \\ i.e., x = nπ / 7 + π / 14; n \in Z \end{array}$

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