Question

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

Answer 1

Given: `cosec θ-cot θ=α` 

We know that, `cosec^2θ-cot^2θ=1` 

Therefore, 

`cosec^2 θ-cot^2θ=1` 

⇒ `(cosec θ+cot θ) (cosec θ-cot θ)=1` 

⇒ `(cosecθ+cot θ )α=1` 

⇒ `(cosec θ+cot θ)=1/α`