c o s e c 2 θ cos 2 θ - 3 cos ⁡ θ + 2 ≥ 1 , if θ belongs to

Question

c o s e c 2 θ cos 2 θ - 3 cos ⁡ θ + 2 ≥ 1 , if θ belongs to, 0 , π 3, π 2 , π, π 3 , π 2, 0 , π 4

MARKS App · Accepted Answer

cos 2 ⁡ θ - 3 cos ⁡ θ + 2 ≥ 1 c o s e c 2 θ = sin 2 ⁡ θ cos 2 ⁡ θ - 3 cos ⁡ θ + 2 ≥ 1 - cos 2 ⁡ θ 2 cos 2 ⁡ θ - 3 cos ⁡ θ + 1 ≥ 0 2 cos ⁡ θ - 1 cos ⁡ θ - 1 ≥ 0 ⇒ cos ⁡ θ ≤ 1 2 or cos ⁡ θ ≥ 1 So, θ ∈ π 3 , π 2 of the given intervals.

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