If cosec θ + cot θ = 5, then cosec θ is equal to _________.

cosec θ + cot θ = 5      ----(1)

{ we know, cosec² θ - cot² θ = 1 }

cosec θ - cot θ = \(\frac{1}{5}\)         -----(2)

On adding equation 1 and 2.

2 cosec θ = 5 + \(\frac{1}{5}\) 

cosec θ = \(\frac{1}{2}\)  [ 5 + \(\frac{1}{5}\) ]