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

sin² θ + cos⁴ θ = cos² θ + sin⁴ θ.

Prove the following trigonometry identity :

(sin θ + cos θ)(cosec θ - sec θ) = cosec θ.sec θ - 2 tan θ

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

sec⁴ A(1 - sin⁴ A) - 2 tan² A = 1.