If 7 sin²θ +3cos²θ=4, then the value of tan θ is (θ is acute) :

 

  1. 1/√2
  2.  1/√3
  3. 1
  4.  √3
Anurag Mishra Professor Asked on 26th October 2015 in Maths.
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  • 1 Answer(s)

    Second option is correct

    Explanation:-

    7 sin²θ + 3 cos²θ = 4
    4 sin²θ + 3 sin²θ + 3 cos²θ = 4
    4 sin²θ + 3 (sin²θ + cos²θ) = 4
    4 sin²θ + 3 = 4
    4 sin²θ = 4 – 3
    4 sin²θ = 1
    sin²θ = 1/4
    Square root on both side,
    sinθ = 1/2
    sinθ = sin 30°
    θ = 30°

    Then, the value of tan 30° = 1/√3

    Hence, the answer is (2) 1/√3

    Monis Rasool Professor Answered on 28th October 2015.
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