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Trigonometry

(i) Factorize the expression 2 sin x cos x - cos x + 4 sin x -2.
(ii) Hence solve the equation 2 sin x cos x - 2=cos x - 4 sin x for -360°≤ x ≤ 360°
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1 Answer

(i) 2 sin x cos x - cos x + 4 sin x -2 = (cos x + 2)(2 sin x - 1)
 
(ii) (cos x + 2)(2 sin x - 1) = 0 ⇒ sin x = 1/2 ⇒ x = 30°, 150°, -330°, -210°.