If - sin θ + cosec θ = 6, then what is the value of sinθ + cosec θ ?

6 $\sqrt{40}$ $\sqrt{34}$ $\sqrt{38}$

$\sqrt{40}$

We are given that :- - sin θ + cosec θ = 6 - sin θ + \(\frac{1}{sinθ}\)= 6 - sin² θ + 1 = 6 sin θ sin² θ + 6 sin θ - 1 = 0 By solving the quadratic equation . we find that , sin θ = ( -3 ± √10 ) Now, sin θ + cosec θ = sin θ + ( 6 +  sin θ ) = 2 sin θ + 6 = 2 ( -3 ± √10 ) + 6 = 2± √10 = √40