Trigonometry

Question

(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°

Answer 1

(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°.