a) (i) Prove the trigonometric identity:
(sin x + cos x)² + (sin x - cos x)² = 2

(ii) Hence, or otherwise, show that:
(sin x + cos x)² = 1 + sin 2x

b) In triangle ABC, AB = 7 cm, BC = 9 cm and angle ABC = 120°.
(i) Calculate the length AC, correct to one decimal place.
(ii) Calculate angle BAC, correct to the nearest degree.
(iii) Calculate the area of triangle ABC, correct to one decimal place.

c) A man standing at a point X observes the top of a vertical pole at an angle of elevation of 36°. He walks 20 m towards the pole to a point Y and observes the top of the pole at an angle of elevation of 54°. Calculate, correct to one decimal place, the height of the pole.

Question

a) (i) Prove the trigonometric identity:
       (sin x + cos x)² + (sin x - cos x)² = 2

(ii) Hence, or otherwise, show that:
       (sin x + cos x)² = 1 + sin 2x

b) In triangle ABC, AB = 7 cm, BC = 9 cm and angle ABC = 120°.
   (i) Calculate the length AC, correct to one decimal place.
   (ii) Calculate angle BAC, correct to the nearest degree.
   (iii) Calculate the area of triangle ABC, correct to one decimal place.

c) A man standing at a point X observes the top of a vertical pole at an angle of elevation of 36°. He walks 20 m towards the pole to a point Y and observes the top of the pole at an angle of elevation of 54°. Calculate, correct to one decimal place, the height of the pole.

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