Solve this: $abs(2cos3x)=1$ ---> (x=... + ...)?

Question

$abs(2cos3x)=1$

Will it be: $x=pi/9+2/3kpi$ AND $x=-pi/9+2/3kpi$
OR ......
$x=pi/9+1/3kpi$ AND $x=-pi/9+1/3kpi$

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Answer 1 · 2017-04-02T15:54:45

$x=2/3kpi+-pi/9$ and $x=2/3kpi+-(2pi)/9$

As $|2cos3x|=1$ , we have

either $2cos3x=1$ i.e. $cos3x=1/2=cos(pi/3)$

and $3x=2kpi+-pi/3$ or $x=2/3kpi+-pi/9$

or $2cos3x=-1$ i.e. $cos3x=-1/2=cos((2pi)/3)$

and $3x=2kpi+-(2pi)/3$ or $x=2/3kpi+-(2pi)/9$