Find the value of cos θ

If sec θ + tan θ = 4, (θ ≠ 900). Then the value of cos θ is

  1. 0
  2. 8/17
  3. 17/8
  4. 4/5
Manish Listener Asked on 19th June 2015 in Maths.
Add Comment
  • 1 Answer(s)

    Answer: (2) 8/17
    Explanation:-
    secθ + tanθ =  4
    1/cosθ + sinθ/cosθ = 4
    (1 + sinθ)/cosθ = 4
    1 + sinθ = 4 cosθ
    squaring on both side,
    (1 + sin)2 = (4cosθ)2
    1 + sin2θ + 2sinθ = 16cos2θ
    1 + sin2θ + 2sinθ = 16(1 – sin2θ)
    1 + sin2θ +2sinθ + 16sin2θ – 16  = 0
    17sin2θ + 2sinθ – 15 = 0
    17sin2θ + 17sinθ – 15sinθ – 15 = 0
    17sinθ(sinθ + 1) – 15(sinθ + 1) = 0
    (sinθ + 1 ) (17sinθ – 15) = 0
    17sinθ – 15 = 0
    17sinθ = 15
    sinθ = 15/17
    height = 15  and hypotenuse = 17
    Then, base2 = 172 – 152
    = 289 – 225 = 64
    base2 = 82
    square root on both side,
    base = 8
    Then, cosθ  = base/hypotenuse
    Therefore, cosθ = 8/17

    Hence, the answer is (2) 8/17.

    Anurag Mishra Professor Answered on 20th June 2015.
    Add Comment
  • Your Answer

    By posting your answer, you agree to the privacy policy and terms of service.