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

RRB Junior Engineer Stage 1 Model Papers 8

Question : 20 of 100

Marks: +1, -0

If θ is a positive acute angle and

4 \cos^2 θ-4 \cos θ+1=0

, then the value of tan (θ – 15°) is equal to

Solution:

4 \cos^2 θ-4 \cos θ+1=0

(2 cos θ-1)^2=0

or,

2 \cos θ=1

⇒ \cos θ=1/2

θ=60°

Hence, the value of

\tan (θ-15°)=\tan (60°-15°)=\tan 45°=1

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