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Question
If 2cos2θ − 11cosθ + 5 = 0 then find possible values of cosθ.
Solution
2cos2θ − 11cosθ + 5 = 0
∴ 2cos2θ − 10cosθ − cosθ + 5 = 0
∴ 2cosθ (cosθ − 5) - 1 (cosθ − 5) = 0
∴ (cosθ − 5)(2cosθ − 1) = 0
∴ cosθ − 5 = 0 or 2cosθ − 1 = 0
∴ cosθ = 5 or cosθ = `1/2`
But − 1 ≤ cosθ ≤ 1 for all θ ∈ R
∴ cosθ ≠ 5
Hence, cosθ = `1/2`.
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