Question

sin2x=sinx

Answer 1

if sin(2x) = sin(x)
then
2x=x there is only one number for which the above is true, it's ZERO.

Also you can say that
sin(2x)=sin(x+x)= sinx cosx+cosx sinx = 2sinxcosx

so,

2 sinx cosx = sinx (cancel sinx on both sides)

2cosx=1
cosx=0.5
x= 60 degrees