prove that (sin theta cos theta = cot theta) is not a trigonometric identity by producing a counterexample

To prove that (sin θ cos θ = cot θ) is not a trigonometric identity.

Assume θ with a value and substitute with it.

Let θ = 45°

So, L. H. S = sin θ cos θ = sin 45° cos 45° = (1/√2) * (1/√2) = 1/2

R. H. S = cot θ = cot 45 = 1

So, L. H. S ≠ R. H. S

So, sin θ cos θ = cot θ is not a trigonometric identity.