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If (cos2θ – 3cosθ + 2) /sin2θ = 1, where 0 < θ < π/2,
which of the following statement(s) is/are correct?
(1) There are two values of θ satisfying the above equation
(2) θ = 60° is satisfied by the above equation.
Select the correct answer using the code given below
  • a)
    1 only
  • b)
    2 only
  • c)
    Both 1 and 2
  • d)
    Neither 1 nor 2
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If (cos2θ – 3cosθ + 2) /sin2θ = 1, where 0 <...
(cos2θ – 3cosθ + 2) /sin2θ = 1
⇒ cos2θ – 3cosθ + 2 = sin2θ
⇒ cos2θ – 3cosθ + 2 = 1 – cos2θ [∵ sin2θ = 1 – cos2θ]
⇒ 2cos2θ – 3cosθ + 1 = 0
⇒ 2cos2θ – 2cosθ – cosθ + 1 = 0
⇒ 2cosθ(cosθ – 1) – 1(cosθ – 1) = 0
⇒ (cosθ – 1) (2cosθ – 1) = 0
⇒ cosθ = 1 or ½
But in the given interval cosθ cannot be 1
⇒ There is only one value satisfying the above equation
⇒ cosθ = ½
∴ θ = 60°
∴ Only 2 is correct.
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Most Upvoted Answer
If (cos2θ – 3cosθ + 2) /sin2θ = 1, where 0 <...
Sorry, but I can't generate a response without the complete information of the equation. Can you please provide the complete equation?
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If (cos2θ – 3cosθ + 2) /sin2θ = 1, where 0 < θ < π/2,which of the following statement(s) is/are correct?(1) There are two values of θ satisfying the above equation(2) θ = 60° is satisfied by the above equation.Select the correct answer using the code given belowa)1 onlyb)2 onlyc)Both 1 and 2d)Neither 1 nor 2Correct answer is option 'B'. Can you explain this answer?
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