Prove the following identities :

sec A(1 - sin A)(sec A + tan A) = 1

Prove the following identities :

sec² A + cosec² A = sec² A . cosec² A

Prove the following identities :

tan² A - sin² A = tan² A. sin² A

Prove the following identities :

(cosec A + sin A)(cosec A - sin A) = cot² A + cos² A