Trigonometry question

Question

Why if

sin(x)=8/5*cos(x/2) then    

sin(x/2)=4/5 is wrong

Answer 1

sin(x)=8/5*sin(x/2)cos(x/2)  = (4/5) sin(x)     {double angle formula}

 

But  sin(x) = 4/5 sin(x)   is only possible if sin(x) = 0.