Explain this trigonometry question please?

2cos(x) = sin(2x)

2cos(x) = 2sin(x)cos(x)

cos(x) = sin(x)cos(x)

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

cos(x) ( 1 - sin(x) ) = 0

So, cos(x) = 0 which means x = pi/2, 3*pi/2 and 5*pi/2  from 0 to 3*pi

and sin(x) = 1 which means x = pi/2 and 5*pi/2 from 0 to 3*pi

Hope this helps.

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