Prove the following identities :

(1 – cosθ)(1+ cosθ)(1+ cot² θ) = 1

Taking LHS = (1 – cosθ)(1+ cosθ)(1+ cot² θ)

Using identity , (a + b) (a – b) = (a² – b²) in first two terms , we get

= (1)² – (cosθ)² (cosec² θ) [∵ cot² θ +1= cosec² θ]

= (1 – cos² θ) (cosec² θ)

= (sin² θ) (cosec² θ) [∵ cos² θ + sin² θ = 1]

=1

= RHS

Hence Proved