Without using trigonometric tables, evaluate the following:

(cos² 25° + cos² 65°) + cosec θ sec(90° - θ) - cot θ tan (90° - θ).

Prove the following identities, where the angles involved are acute angles for which the trigonometric ratios are defined:

(1 + tan² A)(1 - sin A)(1 + sin A) = 1.

Prove the following identities, where the angles involved are acute angles for which the trigonometric ratios are defined:

tan A + cot A = sec A cosec A