If 5sin2 θ = 3(1 + cosθ), 0° < θ < 90°, then the value of cosecθ + cotθ is :
Answer & explanation
Correct answer: option 4
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
= \(\frac{5}{√21}\) + \(\frac{2}{√21}\)
= \(\frac{7}{√21}\)
= \(\frac{√7}{√3}\)