# Find the value of cos θ

If sec θ + tan θ = 4, (θ ≠ 90^{0}). Then the value of cos θ is

- 0
- 8/17
- 17/8
- 4/5

**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 + sin^{2}θ + 2sinθ = 16cos^{2}θ

1 + sin^{2}θ + 2sinθ = 16(1 – sin^{2}θ)

1 + sin^{2}θ +2sinθ + 16sin^{2}θ – 16 = 0

17sin^{2}θ + 2sinθ – 15 = 0

17sin^{2}θ + 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, base^{2} = 17^{2} – 15^{2}

= 289 – 225 = 64^{
}base^{2} = 8^{2}

square root on both side,

base = 8

Then, cosθ = base/hypotenuse

Therefore, cosθ = 8/17

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