Show that

Using trigonometric identities,

cosec θ = 1/sin θ & cot θ = cos θ/sin θ

LHS = (cosec θ – cot θ)²

As we know, sin² θ = 1 – cos² θ

And (1 – cos² θ) = (1 + cos θ)(1 – cos θ) [by (a² – b²) = (a + b)(a – b)]

⇒ sin² θ = (1 + cos θ)(1 – cos θ) …(i)

So, using equation (i),

LHS = (cosec θ – cot θ)² =

= RHS

Hence, we have got

(cosec θ – cot θ)² = .