If 2cotθ = 3, then (√(13) Cosθ – 3tanθ)/(3tanθ + √(13) Sinθ) is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e 1 / 4
⇒ 2cotθ = 3
⇒ cotθ = 3 / 2
By the identity, 1 + cot2θ = cosec2θ
⇒ cosec2θ = 1 + (9 / 4)
⇒ cosecθ = √13 / 2
⇒ sinθ = 2 / √13
By the identity, sin2θ + cos2θ = 1
⇒ 4 / 13 + cos2θ = 1
⇒ cosθ = 3 / √13
⇒ (√(13) Cosθ – 3tanθ)/(3tanθ + √(13) Sinθ)
⇒ (√(13) × (3 / √13) – 3 × (2 / 3))/(3 × (2 / 3) + √(13) × (2 / √13))
⇒ (3 - 2) / (2 + 2)
⇒ 1 / 4