SSC CHSL Model Paper 4

8 sin x = 4 + cos x
8 sin x – 4 = cos x
Squaring both the sides, we get:
64 sin${}^2$x + 16 – 64 sin x = cos${}^2$x
⇒ 64 sin${}^2$x + 16 – 64 sin x = 1 – sin${}^2$x
⇒ 65 sin${}^2$x – 64 sin x + 15 = 0
⇒ 65 sin${}^2$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 = $\frac{3}{5},\frac{5}{13}$