If cosec θ − cot θ = α, write the value of cosec θ + cot α.

Given: cosec θ – cot θ = α ………………(i)

To find: cosec θ + cot θ

We know that 1 + cot² θ = cosec² θ

⇒ 1 = cosec² θ – cot² θ

Now, ∵ a² – b² = (a – b) (a + b)

⇒ 1 = cosec² θ – cot² θ = (cosec θ – cot θ) (cosec θ + cot θ)

⇒ From (i), we have

1 = α (cosec θ + cot θ)