If α is a root of 25cos2 θ + 5cos θ – 12 = 0, π/2 < α < π, the

1.	If α is a root of 25cos2 θ + 5cos θ – 12 = 0, π/2 < α < π, then sin 2α is equal to(A) -24/25(B) -13/18(C) 13/18(D) 24/25
Answer» Correct option is : (A) -24/25 25 cos² θ + 5 cos θ – 12 = 0 ∴ (5cos θ + 4) (5 cos θ – 3) = 0 ∴ cos θ = -4/5 or cos θ = 3/5 Since π/2 < α < π, cos α < 0 ∴ cos α = -4/5 sin² α = 1 – cos² α = 1 – 16/25 = 9/25 ∴ sin α = ± 3/5 Since π/2 < α < π sin α > 0 ∴ sin α = 3/5 sin 2 α = 2 sin α cos α = 2 (3/5) (-4/5) = -24/25

If α is a root of 25cos2 θ + 5cos θ – 12 = 0, π/2 < α < π, then sin 2α is equal to(A) -24/25(B) -13/18(C) 13/18(D) 24/25

Answer»

Correct option is : (A) -24/25

25 cos² θ + 5 cos θ – 12 = 0

∴ (5cos θ + 4) (5 cos θ – 3) = 0

∴ cos θ = -4/5 or cos θ = 3/5

Since π/2 < α < π,

cos α < 0

∴ cos α = -4/5

sin² α = 1 – cos² α = 1 – 16/25 = 9/25

∴ sin α = ± 3/5

Since π/2 < α < π sin α > 0

∴ sin α = 3/5

sin 2 α = 2 sin α cos α

= 2 (3/5) (-4/5) = -24/25