Algebra cos(2arcsin1/2) =

= 1- 2sin^2(arcs in 1/2)= 1/2

cos(2arcsin1/2)=1-2sin² (arcsin1/2)= 1-2 *(1/2)²=1-1/2=1/2
cos 2x= cos²x-sin²x=1-2sin²x
sin (arcsinx)=x