The general solution of the equation cos⁡xcos⁡6x=−1, is

# The general solution of the equation $\mathrm{cos}x\mathrm{cos}6x=-1$, is

1. A

$x=\left(2n+1\right)\pi ,n\in Z$

2. B

$x=2n\pi ,n\in Z$

3. C

$x=\left(2n-1\right)\pi ,n\in Z$

4. D

none of these

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### Solution:

We have,

and

The value of x satisfying these two equations simultaneously and lying between 0 and 2 $\mathrm{\pi }$ is $\mathrm{\pi }$. Therefore, the general solution is given by

$x=2n\pi +\pi ,n\in Z⇒x=\left(2n+1\right)\pi ,n\in Z$

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