The equation cos x cos 6x = -1:

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has 50 solutions in $[0, 100 π]$

has 3 solutions in $[0, 3 π]$

has even number of solutions in $(3 π, 13 π)$

has one solution in $[\frac{π}{2}, π]$

answer is A, C, D.

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Detailed Solution

cosx cos6x = -1
$\Rightarrow$ $\begin{array}{l} \underset{↓}{\cos 6 x} = \underset{↓}{- \sec x} \\ [- 1, 1] [- \infty, - 1] \cup [1, \infty] \end{array}$
$\Rightarrow$ $\begin{array}{l} \underset{&}{\cos 6 x = - 1} \\ \cos x = 1 \end{array}$ OR $\begin{array}{l} \underset{&}{\cos 6 x = 1} \\ \cos x = - 1 \end{array}$

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