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.