Find all values to sin(2x)-cos(x)

and also find all the values to tan(x)=1

i'm assuming the first one is equal to 0?
sin (2x) - cos (x) =0
2sinxcosx - cosx =0
cosx (2sinx - 1) = 0
cosx=0 and 2sinx-1=0
x= π/2, 3π/2, π/6, 5π/6

tanx = 1
x=π/4, 5π/4

As, sin2x = 2sinx cosx
so, 2sinXcosX - cosX = 0
looking at this, we have a cosX in both terms so we can factorise.... solving any equation we are always looking to factorise:
cosX(2sinX-1) = 0
which means that either

cosX=0 or 2sinX-1 = 0
cosX=0 or 2sinX = 1
cosX=0 or sinX = 1/2
X=90 or X=30... in the first quadrant.

There are other angles that give these answers too but you do not quote the range of angles acceptable.