8 sin x 4 cos x the values of sin x are ........

Quantitative Aptitude ( CCS) Trignometry

8 sin x = 4 + cos x, the values of sin x are :

3/5 , –5/13

–3/5, 5/13

–3/5, –5/13

3/5, 5/13

8 sin x – 4 = cos x ⇒ 8 sin x – 4 =

1 – sin2 x

⇒ 1 – sin2 x = (8 sin x – 4)2

⇒ 1 – sin2 x = 64 sin2 x + 16 – 64 sin x

⇒ 65 sin2 x – 64 sin x + 15 = 0

⇒ 65 sin2 x – 39 sin x – 25 sin x + 15 = 0

⇒ 13 sin x (5 sin x – 3) – 5 (5 sin x – 3) = 0

⇒ (5 sin x – 3) (13 sin x – 5) =0

⇒ sin x =3/5 or sin x = 5/13

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