If 5sin² θ = 3(1 + cosθ), 0° < θ < 90°, then the value of cosecθ + cotθ is :

$\sqrt{\frac{7}{3}}$

5sin² θ = 3(1 + cosθ)

{ sin² θ + cos² θ  = 1 }

5 ( 1 - cos² θ) = 3(1 + cosθ)

5 ( 1 - cos θ) = 3

cos θ = \(\frac{2}{5}\)

By using pythagoras theorem ,

P² + B² = H²

P² + 2² = 5²

P = \(\sqrt {21 }\)

ATQ,

 cosecθ + cotθ

= \(\frac{5}{√21}\) + \(\frac{2}{√21}\)

= \(\frac{7}{√21}\)

= \(\frac{√7}{√3}\)