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)