If cosec θ + cot θ = 2, then sin θ is :

cosec θ + cot θ = 2      -----(1)

{ we know, cosec²θ - cot²θ = 1 }

so, cosec θ -  cot θ = \(\frac{1 }{cosec θ + cot θ}\)

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

Adding equation 1 and 2.

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

cosec θ = \(\frac{5 }{4}\)

{ we know,  sin θ = \(\frac{1 }{cosec θ}\) }

so, sin θ = \(\frac{4 }{5}\)