Solve the following equation. θ : 2 cos² θ + (4 + √(3) ) sin θ - 2(1 + √(3) ) = 0 where θ is an acute angle.

Solve the following equation. θ : 2 cos² θ + (4 + √(3) )…

Solve the following equation.

$\theta$ : 2 cos² $\theta$ + (4 + $\sqrt{3}$ ) sin $\theta$ - 2(1 + $\sqrt{3}$ ) = 0 where $\theta$ is an acute angle.

Show answer & explanation

Correct answer: D

Explanation

The correct answer is option 4 i.e. 60º

2cos²θ + (4+√3) sinθ - 2(1+√3) = 0

⇒ 2(1-sin²θ) + 4sinθ + √3sinθ - 2 - 2√3 = 0 (∵ 1-sin²θ = cos²θ )

⇒ 2 - 2sin²θ + 4sinθ + √3sinθ - 2 - 2√3 = 0

⇒ 2sin²θ - 4sinθ - √3sinθ + 2√3 = 0

⇒ 2sin²θ - (4+√3)sinθ + 2√3 = 0

⇒ 2sin²θ - 4sinθ - √3sinθ + 2√3 = 0

⇒ 2sinθ(sinθ -2°) - √3(sinθ -2) = 0

⇒ 2sinθ = √3 or (∵ sinθ = 2 is not possible)

⇒ Sinθ = √3/2

⇒ θ = 60°