Find the general solution for the equation: cos 4x = cos 2x - Vidyadip

Question

Find the general solution for the equation: cos 4x = cos 2x

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Answer

Here cos 4x = cos 2x
$ \Rightarrow 4x = 2n\pi \pm 2x,n \in Z$ [ $\because$ If cos x = cos y $ \Rightarrow x = 2n\;\pi \pm y$]
$ \Rightarrow 4x - 2x = 2n\;\pi $ or $4x + 2x = 2\;\pi ,n \in Z$
$ \Rightarrow 2x = 2n\;\pi $ or $6x = 2n\;\pi ,n \in Z$
$ \Rightarrow x = 2\pi $ or $x = \frac{{n\pi }}{3},n \in Z$
Hence general solutions are $n\pi $ or $\frac{{n\pi }}{3},n \in Z$

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