Evaluate x and y from the given figure.

In the given figure, △ABC is right angled at B.

If AC = 20 cm and tan A = $\dfrac{3}{4}$, find the lengths of AB and BC.

Without using trigonometric table, find the values of:

(i) sin 60° cos 30° + cos 60° sin 30°

(ii) sin 45° cos 30° - cos 45° sin 30°

(iii) cos 60° cos 45° + sin 60° sin 45°

(iv) cos 90° + cos² 45° sin 30° tan 45°

Without using trigonometric tables, find the values of;

(i) (3sin² 45° + 2cos²60°)

(ii) (3cos² 30° + tan²60°)

(iii) (cos 0° + sin 45° + sin 30°)(sin 90° - cos 45° + cos 60°)

(iv) 2 $\sqrt{2}$ cos 45°cos 60° + 2 $\sqrt{3}$ sin 30° tan 60° - cos 0°

(v) $\dfrac{4}{3}$ tan²30°+ sin²60° - 3 cos²60°+ $\dfrac{3}{4}$ tan²60°- 2 tan²45°

(vi) $\dfrac{\sin^2 45^\circ + \cos^2 45^\circ}{\tan^2 60^\circ}$