use an apropriate sum or difference indentity to prove the double-angle identity cos2u=1-2sin2u

Answer 1

You stated the identity incorrectly , is should have been
cos 2u = 1 - 2sin^2 u

LS = cos 2u
= cos(u+u) = cosucosu - sinusinu
= cos^2 u - sin^2 u
= (1-sin^2 u) - sin^2 u
= 1 - 2sin^2 u
= RS