Show that : Cos^-1x = 2sin ^-1 sqrt(1-x/2)

Start by R.H.S.   2Sin^-1(√(1-X/2)
Now put x=cos2$\theta$
=   2Sin^-1(√(1-cos2$\theta$/2) 
Since 1-cos2$\theta$ = 2sin²$\theta$ so put this value we get 
 =2sin^-1(2sin²$\theta$/2 )
=2sin^-1sin$\theta$ 
=2$\theta$ 
=cos^-1x =L.H.S