Question

If sin2θ = √3cosθ and 0 < θ < 90°, then, [cosθ + √3cosecθ + √3tanθ + √3cotθ] is equal to – 

1. 17/6
2. 13/6
3. 12/5
4. 11/5

Answer 1

Correct Answer - Option 2 : 13/6

Given:

 sin2θ = √3cosθ

Formula used:

sin2θ = 2sinθcosθ

Calculation:

Given, sin2θ = √3 cosθ

⇒ 2sinθ cosθ = √3cos θ

⇒ sinθ = √3/2

⇒ θ = 60°

 [cosθ + √3cosecθ + √3tanθ + cotθ]

⇒ [cos60° + √3cosec60° + √3tan60° + √3cot60°]

⇒ [1/2 + √3(2/√3) + √3(√3) + √3/√3]

⇒ [1/2 + 2 + 3 + 1]

⇒ [1/2 + 6]

⇒ 13/6