If 4sin²θ = 3(1 + cosθ ), 0° θ √15tanθ + 4/(√15) sinθ + 2secθ ?

If 4sin²θ = 3(1 + cosθ ), 0° θ √15tanθ + 4/(√15) sinθ +…

If 4sin²θ = 3(1 + cosθ ), 0° < θ < 90° Then what is the value of √15tanθ + $\frac{4 }{√15}$ sinθ + 2secθ ?

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Correct answer: B

Explanation

The correct answer is option 2 i.e. 24.

Sin²θ + cos²θ = 1

Hence, 4(1 - cos²θ) = 3(1 + cosθ)

⇒ 4(1 + cosθ)(1 - cosθ) = 3(1 + cosθ)

⇒ $\frac{3}{4}$ = 1 - cosθ

⇒ cosθ = $\frac{1}{4}$

Hence, sinθ = $\frac{√15}{ 4}$

⇒ Secθ = 4

⇒ Tanθ = √15

Substituing the values we get

√15tanθ + $\frac{4 }{√15}$ sinθ + 2secθ = 15 + 1 + 8 = 24