Show that:

(i)

(ii)

(sin²30° + 4 cot²45° — sec²60°)(cosec²45° sec²30°)

Verify each of the following:

(i) sin 60° cos 30° — cos 60° sin 30° = sin 30°

(ii) cos 60° cos 30° + sin 60° sin 30° = cos 30°

(iii) 2 sin 30° cos 30° = sin 60°

(iv) 2 sin 45° cos 45° = sin 90°

If A = 45°, verify that:

(i) sin 2A = 2 sin A cos A

(ii) cos 2A = 2 cos²A —1 = 1— 2 sin²A