Correct Answer - Option 4 :
\(\frac{{1 - 2\surd 3}}{2}\)
Given:
4 - 2sin2θ - 5cosθ = 0
Formula used:
sin2θ + cos2θ = 1
Calculation:
4 - 2sin2θ - 5cosθ = 0
⇒ 4 - 2(1 - cos2θ ) - 5cosθ = 0
⇒ 4 - 2 - 2cos2θ - 5cosθ = 0
⇒ 2cos2θ - 5cosθ + 2 = 0
⇒ cosθ = [5 ± √(25 - 16)]/4
⇒ cosθ = (5 ± 3)/4
⇒ cosθ = 2 or 1/2
cosθ can't more than 1, cosθ = 1/2
tanθ = √3
cosθ - tanθ
⇒ (1/2) - √3
⇒ \(\frac{{1 - 2\surd 3}}{2}\)
∴ The value is \(\frac{{1 - 2\surd 3}}{2}\).