Prove the following identities :

(1 + tan A + sec A)(1 + cot A - cosec A) = 2

If 2 sin A - 1 = 0, show that :

sin 3A = 3 sin A - 4 sin³ A

If 4 cos² A - 3 = 0, show that :

cos 3A = 4 cos³ A - 3 cos A