sin(2x) doesn't come into use here, this is a factorising question
Take cos(x) from both sides:
Factor out cos(x):
Since cos(x) is symmetrical about then is also a solution
Also note that because 2sin(x) is symmetrical about pi/2 then it follows that there is another root at .
Therefore the equation 2sin(x)cos(x) = cos(x) has roots of
Divide through by cos(x)
Note that method 1 is better because it yielded two extra solutions