The general solution of cos 4theta = cos 3the | vedclass

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Question

(A) Given equation: $\cos 4	heta = \cos 3	heta$.Using the general solution formula for $\cos x = \cos y$, which is $x = 2n\pi \pm y$ where $n \in Z$

Vedclass · Accepted Answer

$\frac{2n\pi}{7}, n \in Z$

Vedclass · Answer

(A) Given equation: $\cos 4	heta = \cos 3	heta$.Using the general solution formula for $\cos x = \cos y$, which is $x = 2n\pi \pm y$ where $n \in Z$.Here, $x = 4	heta$ and $y = 3	heta$.Case $1$: $4	heta = 2n\pi + 3	heta \implies 	heta = 2n\pi$.Case $2$: $4	heta = 2n\pi - 3	heta \implies 7	heta = 2n\pi \implies 	heta = \frac{2n\pi}{7}$.Since $	heta = 2n\pi$ is a subset of $	heta = \frac{2n\pi}{7}$ (when $n$ is a multiple of $7$), the general solution is $	heta = \frac{2n\pi}{7}, n \in Z$.

The general solution of $\cos 4\theta = \cos 3\theta$ is $\theta =.....$

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