If sin θ=√(3)cosθ , then what is the value of (3sin²θ+cosθ)/(2cosθ+5) ?

If sin θ=√(3)cosθ , then what is the value of…

If $sin \theta=\sqrt{3}cos\theta$ , then what is the value of $\frac{3sin^{2}\theta+cos\theta}{2cos\theta+5}$ ?

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 11/24.

sin θ = √3 cos θ

⇒ sin θ/cos θ = tan θ = √3

⇒ θ = 60°

Now, (3 sin²θ + cos θ)/(2 cos θ + 5)

= (3 sin²60° + cos 60°)/(2 cos 60° + 5)

= [3(√3/2)² + 1/2]/[2 × 1/2 + 5]

= (3 × 3/4 + 1/2)/(1 + 5)

= (9/4 + 1/2)/6

= (11/4)/6

= 11/24