# Find the Value of Positive Acute Angle

If θ is a positive acute angle and 4 cos^{2} θ – 4 cos θ + 1 = 0, then the value of tan (θ – 15^{0}) is equal to

- 0
- 1
- √3
- 1/√3

**Answer: (2) 1**

**Explanation:-**

4 cos^{2} θ – 4 cos θ + 1 = 0,

4 cos^{2} θ – 4 cos θ + 1 = 0

4 cos^{2} 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 60^{o}

θ = 60^{o}

then, tan(θ – 15^{o}) = tan (60^{o} – 15^{o})

tan45^{0} = 1

Hence, the answer is (2) 1.