If 12cos2θ - 2sin2θ + 3cosθ = 3, 0o < θ < 90o, then what is the value of (cosecθ + secθ)/(tanθ + cotθ) ?
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Correct answer: D
Explanation
The correct answer is option 4 i.e (1 + √(3))/(2)
⇒ 12cos2θ - 2sin2θ + 3cosθ = 3
⇒ 12cos2θ - 2(1 - cos2θ) + 3cosθ = 3
⇒ 14cos2θ + 3cosθ - 5 = 0
We will now solve the given quadratic equation.
⇒ (cosθ - 1 / 2)(cosθ + 5 / 7)
As the angle is in the first quadrant so the cosθ will be positive.
⇒ cosθ = 1 / 2 ⇔ θ = 60°
⇒ (cosecθ + secθ)/(tanθ + cotθ)
⇒ sinθ + cosθ ⇔ (1 + √(3))/(2)