We have to prove that (sin x)^2 * [ 1 + (cot x)^2] = 1

(sin x)^2 * [ 1 + (cot x)^2]

=> (sin x)^2 * [ 1 + (cos x)^2/ (sin x)^2]

=> (sin x)^2 * [ (sin x)^2 + (cos x)^2]/ (sin x)^2

=> (sin x)^2 + (cos x)^2

=> 1

**This proves that (sin x)^2 * [ 1 + (cot x)^2] = 1**