Choose the correct option and justify your choice: (i) \( \frac{2 \tan 30^\circ}{1 + \tan^2 30^\circ} \) (A) \( \sin 60^\circ \) (B) \( \cos 60^\circ \) (C) \( \tan 60^\circ \) (D) \( \sin 30^\circ \) (ii) \( \frac{1 - \tan^2 45^\circ}{1 + \tan^2 45^\circ} \) (A) \( \tan 90^\circ \) (B) 1 (C) \( \sin 45^\circ \) (D) 0 (iii) \( \sin 2A = 2 \sin A \) is true when \( A = \) (A) 0° (B) 30° (C) 45° (D) 60° (iv) \( \frac{2 \tan 30^\circ}{1 - \tan^2 30^\circ} \) (A) \( \cos 60^\circ \) (B) \( \sin 60^\circ \) (C) \( \tan 60^\circ \) (D) \( \sin 30^\circ \)