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Question

3tan θ + cot θ = 5 cosec θ. Solve for θ,0 <θ 90.

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Solution

3sinθcosθ + cosθsinθ = 5sinθ

sinθ ( 3sin2θ + cos2θ) = 5 sinθ cosθ

3(1 - cos2θ) + cos2θ = 5 cosθ

2cos2θ + 5cosθ - 3 = 0

2cosθ [cosθ + 3] - 1(cosθ + 3) = 0

(cosθ + 3) (2cosθ - 1) = 0

cosθ = -3 or cosθ = 12

cosθ = -3 not possible.
Hence θ = 60 from cosθ = 12


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