Question
3tanθ + cotθ = 5cosecθ. Solve for θ, 0≤θ≤90.
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Answer:
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3sinθcosθ+cosθsinθ =5sinθ
3sin2θ+cos2θsinθcosθ=5sinθ
3sin2θ+cos2θ=5cosθ
3(1 -cos2θ) +cos2θ = 5cosθ
2cos2θ + 5cosθ - 3 = 0
2cosθ[cosθ + 3] - 1(cosθ + 3) = 0
(cosθ + 3) (2cosθ - 1) = 0
cosθ= -3 or cosθ = 12
Note that cosθ= -3 is not possible as−1≤cosθ≤1
Thus, θ = 60∘
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:
3sinθcosθ+cosθsinθ =5sinθ
3sin2θ+cos2θsinθcosθ=5sinθ
3sin2θ+cos2θ=5cosθ
3(1 -cos2θ) +cos2θ = 5cosθ
2cos2θ + 5cosθ - 3 = 0
2cosθ[cosθ + 3] - 1(cosθ + 3) = 0
(cosθ + 3) (2cosθ - 1) = 0
cosθ= -3 or cosθ = 12
Note that cosθ= -3 is not possible as−1≤cosθ≤1
Thus, θ = 60∘
Was this answer helpful ?
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