If 0° < θ < 90° and cos2 θ = 3 (cot2 θ - cos2 θ) then the value of (1/2 × secθ + sinθ)-1 is:
Show answer & explanation
Correct answer: B
Explanation
Correct Answer is option 2 i.e. 2(2 – √3)
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Cot θ = Cosθ/Sinθ or Cosθ × Cosecθ Cosec2θ – 1 = Cot2θ |
Given Cos2θ = 3(Cot2θ - Cos2θ) Where 0° < θ < 90° |
Cos2θ = 3(Cot2θ - Cos2θ) ⇒ Cos2θ = 3Cos2θ(Cosec2θ – 1) ⇒ 1 = 3Cot2θ ⇒ Cotθ = 1/√3 ⇒ θ = 60° Now, (1/2 × Secθ + Sinθ)-1 Put θ = 60° ⇒ (1/2 × Sec60 + Sin60)-1 ⇒ (1/2 × 2 + √3/2)-1 ⇒ [(2 + √3)/2]-1 ⇒ 2/(2 + √3) ⇒ [2/(2 + √3)] × [(2 - √3)/(2 - √3)] ⇒ 2(2 - √3) |