Find A, if 0° ≤ A ≤ 90° and :

(i) 2 cos² A - 1 = 0

(ii) sin 3A - 1 = 0

(iii) 4 sin² A - 3 = 0

(iv) cos² A - cos A = 0

(v) 2 cos² A + cos A - 1 = 0

Prove that :

(cosec A - sin A)(sec A - cos A) sec² A = tan A

Prove the identity (sin θ + cos θ)(tan θ + cot θ) = sec θ + cosec θ.