1.

If 2cos2 θ – 11 cos θ + 5 = 0, then find the possible values of cos θ.

Answer»

2cos2 θ – 11 cos θ + 5 = 0

∴ 2cos2 θ – 10 cos θ – cos θ + 5 = 0 

∴ 2cos θ(cos θ – 5) – 1 (cos θ – 5) = 0 

∴ (cos θ – 5) (2cos θ – 1) = 0 cos θ – 5 = 0 or 2cos θ – 1 = 0 

∴ cos θ = 5 or cos θ = 1/2 

Since, -1 ≤ cos θ ≤ 1 

∴ cos θ = 1/2



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