If sin^2 θ = cos^3 θ, then the value of (cot^2 θ − cot^6 θ) is:

We are given that :-

sin²θ = cos³θ   ----(1)

Now,

cot²θ - cot6 θ

= cot²θ - \(\frac{cos6  θ}{sin6 θ}\)

{ on squaring equation 1 , sin4 θ = cos6 θ }

= cot²θ - \(\frac{sin4 θ}{sin6 θ}\)

= cot²θ - \(\frac{1}{sin² θ}\)

= cot²θ - cosec²θ

{ using , cosec²θ - cot²θ = 1 }

= - 1