`tan(2x)-2cos(x)=0, 0<=x<=2pi`

`tan(2x)-2cos(x)=0`

`sin(2x)/cos(2x)-2cos(x)=0`

`sin(2x)-2cos(2x)cos(x)=0`

`2sin(x)cos(x)-2cos(2x)cos(x)=0`

`2cos(x)(sin(x)-cos(2x))=0`

using the identity`cos(2x)=1-2sin^2(x),`

`2cos(x)(sin(x)-(1-2sin^2(x)))=0`

`2cos(x)(sin(x)-1+2sin^2(x))=0`

solving each part...

(The entire section contains 181 words.)

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