trigonometric function m2 15pt

1.cos3x=4cos^3 x-3cosx
express cos72 in surd form
2.by using sin3x=3sinx-4sin^3 x and
2sin54degree=1+2sin18degree
show that sin18degree=(root5 -1)/4
3.after expressing tan3x in terms of tanx, express tan72degree in surd form
my problem:why tanx=root(5-2root5) is rejected?
4.by considering cos36=(root5 +1)/4, express sin 18degree in surd form
ans:(root5 -1)/4
my problem: why i get (root(3-root5))/(2root2)
please also show how to get :(root5 -1)/4