If 2sin2 θ + 3sin θ = 0, find the permissible values of cosθ.

1.	If 2sin2 θ + 3sin θ = 0, find the permissible values of cosθ.
Answer» 2sin² θ + 3sin θ = 0 ∴ sin θ (2sin θ + 3) = 0 ∴ sin θ = 0 or sin θ = \(\frac {-3}{2}\) Since – 1 ≤ sin θ ≤ 1, sin θ = 0 \(\sqrt{1-\cos^2 \theta} =0\)...[∴ sin² θ = 1-cos²θ] ∴ 1- cos²θ = 0 ∴ cos²θ = 1 ∴ cos θ = ±1 …[∵ – 1 ≤ cos θ ≤ 1]

Answer»

2sin² θ + 3sin θ = 0

∴ sin θ (2sin θ + 3) = 0

∴ sin θ = 0 or sin θ = \(\frac {-3}{2}\)

Since – 1 ≤ sin θ ≤ 1,

sin θ = 0

\(\sqrt{1-\cos^2 \theta} =0\)...[∴ sin² θ = 1-cos²θ]

∴ 1- cos²θ = 0

∴ cos²θ = 1

∴ cos θ = ±1 …[∵ – 1 ≤ cos θ ≤ 1]

Discussion