If cosA = 1/2(a+1/a) then prove cos2A=1/2(a^2 +1/a^2)

if cosA=1/2(a+1/a) then show that cos2A=1/2(a2+1/a2)

If cosA = 1/2(a+1/a) then prove cos2A=1/2(a^2 +1/a^2)

If cosx=1,2(a+1,a), show that cos2x=1,2(a^2+1,(a^2))