SSC CPO 2020 PYQ — Question 109

The correct answer is Option 4 i.e   $\frac{1-2\sqrt3}{2}$​​​​​​​​​​​​​​​​​​​​​.

Given:

4 - 2sin²θ - 5cosθ = 0

Identity used:

sin²θ = 1 - cos²θ

Calculation:

⇒ 4 - 2sin²θ - 5cosθ = 0

⇒ 4 - 2 × (1 - cos²θ) - 5cosθ = 0

⇒ 4 - 2 + 2cos²θ - 5cosθ = 0

⇒ 2cos²θ - 5cosθ + 2 = 0

⇒ 2cos²θ - 4cosθ - cosθ + 2 = 0

⇒ 2cosθ × (cosθ - 2) - 1 × (cosθ - 2) = 0

⇒ (2cosθ - 1) × (cosθ - 2) = 0

⇒ cosθ = 1/2 and cosθ = 2

Rejecting cosθ = 2 as 0° < θ < 90°

So, cosθ will be 1/2

⇒ θ = 60°

Thus, The value of cosθ - tanθ 

⇒ cos 60° - tan 60°

⇒ 1/2 - √3

⇒ $\frac{1-2\sqrt3}{2}$​​​​​​​