If sin 3A = 1 and 0 ≤ A ≤ 90°, find :

(i) sin A

(ii) cos 2 A

(iii) tan² A - $\dfrac{1}{\text{cos}^2 \text{ A}}$

If 2 cos 2A = ${\sqrt3}$ and A is acute, find :

(i) A

(ii) sin 3A

(iii) sin² (75° - A) + cos² (45° + A)

Evaluate :

$\dfrac{\text{cos 3 A - 2 cos 4 A}}{\text{sin 3 A + 2 sin 4 A}}$, when A = 15°.

Evaluate :

$\dfrac{\text{3 sin 3 B + 2 cos(2 B + 5°)}}{\text{2 cos 3 B - sin(2 B - 10°)}}$; when B = 20°.