(tan A + cot A)(cosec A - sin A)(sec A - cos A) = 1

If 4 cos² A - 3 = 0 and 0° ≤ A ≤ 90°; then prove that :

(i) sin 3A = 3 sin A - 4 sin³ A

(ii) cos 3A = 4 cos³ A - 3 cos A

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