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

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