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

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(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 \m

Vedclass · Accepted Answer

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

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(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 $n \in \mathbb{Z}$.Here, $x = 4	heta$ and $y = 3	heta$.Case $1$: $4	heta = 2n\pi + 3	heta \implies 	heta = 2n\pi$.Case $2$: $4	heta = 2n\pi - 3	heta \implies 7	heta = 2n\pi \implies 	heta = \frac{2n\pi}{7}$.Thus, the general solution is $	heta = 2n\pi$ or $	heta = \frac{2n\pi}{7}$ for $n \in \mathbb{Z}$.

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

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