Find the Value of Positive Acute Angle

If θ is a positive acute angle and 4 cos2 θ – 4 cos θ + 1 = 0, then the value of tan (θ – 150) is equal to

1. 0
2. 1
3. √3
4. 1/√3
Manish Listener Asked on 22nd July 2015 in

Explanation:-
4 cos2 θ – 4 cos θ + 1 = 0,
4 cos2 θ – 4 cos θ + 1 = 0
4 cos2 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 60o
θ = 60o
then, tan(θ – 15o) = tan (60o – 15o)
tan450 = 1
Hence, the answer is (2) 1.

Anurag Mishra Professor Answered on 22nd July 2015.