Demonstre as identidades seguintes:

a) Cos^2 x = cotg^2 x/ 1 + cotg^2 x

b) sen x × tg x + cos x = sec x

c) tg x + cotg x = sec x × cossec x

d) tg x + cos x / 1 + sen x = sec x

e) Sen x + cos x / sen x - cos x = 1 + cotg x / 1 - cotg x