Question

give the most general solutions to the equation 2sinxcosx-sin(2x)cos(2x)=0

Answer 1

Make 2sinxcosx to sin(2x) then factor out sin2x and solve. :)

Answer 2

Sin2X(1-Cos2X)=0

either Sin2X=0 which follows 2X=n*pie or x=n*pie/2 n=0 onwards integers
or Cos2X=1 which follows 2X=2n*pie or x=n*pie n=0 onwards integers

so our solution is union of the two above.