ABC is an isosceles right-angled triangle. Assuming AB = BC = x, find the value of each of the following trigonometric ratios :
(i) sin 45°
(ii) cos 45°
(iii) tan 45°

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Prove that :
sin 60° = 2 sin 30° cos 30°.

Prove that :
4 (sin⁴ 30° + cos⁴ 60°) - 3 (cos² 45° - sin² 90°) = 2