Find the Value of Positive Acute Angle

If θ is a positive acute angle and 4 cos2 θ – 4 cos θ + 1 = 0, then the value of tan (θ – 150) is equal to

  1. 0
  2. 1
  3. √3
  4. 1/√3
Manish Listener Asked on 22nd July 2015 in Maths.
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  • 1 Answer(s)

    Answer: (2) 1
    Explanation:-
    4 cos2 θ – 4 cos θ + 1 = 0,
    4 cos2 θ – 4 cos θ + 1 = 0
    4 cos2 θ – 2 cos θ – 2 cos θ + 1 = 0
    2 cos θ (2 cos θ – 1) – 1(2 cos θ – 1) = 0
    (2 cos θ – 1) (2 cos θ – 1) = 0
    (2 cos θ – 1)2 = 0
    2 cos θ – 1 = 0
    2 cos θ = 1
    cos θ = ½
    cos θ = cos 60o
    θ = 60o
    then, tan(θ – 15o) = tan (60o – 15o)
    tan450 = 1
    Hence, the answer is (2) 1.

    Anurag Mishra Professor Answered on 22nd July 2015.
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