If cosec θ + cot θ = 2, then what is the value of cosec θ?

As , cosecθ + cotθ = 2   ----(1)

then cosec θ - cotθ = \(\frac{1}{2}\)     -----(2)

Adding 1 & 2

2cosecθ = 2 + \(\frac{1}{2}\) = \(\frac{5}{2}\)

cosecθ = \(\frac{5}{4}\)

So , cosec θ  = \(\frac{5}{4}\)