If sinθ = √3 cosθ , 0° < θ < 90°, then the value of 2sin²θ + sec²θ + sinθsecθ + cosecθ is?
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Correct answer: A
Explanation
The correct answer is option 1 i.e. (33 + 10√3)/6
sinθ = √3cosθ
⇒ sinθ/cosθ = √3
⇒ tanθ = √3
⇒ θ = 60°
Now, substitute the value of θ = 60° in the given equation:
⇒ 2 × sin²60° + sec² 60°+ sin60°× sec60° + cosec60°
⇒ 2 × (3/4) + 4 + (√3/2) × 2 + (2/√3)
⇒ (33 + 10√3)/6