If $$cot^4x + cot^2x = 1$$​, then the value of $$cosec^4x - cosec^2x$$ is:

Correct option is A

Given: 

$$\cot^4 x + \cot^2 x = 1$$​​

Concept Used; 

$$\cosec^2 x = 1 + \cot^2 x$$ 

cosec²x - 1 = cot²x  

(a -b)^2​ = a²+ b²-2ab

Solution: 

$$\cot^4 x + \cot^2 x = 1$$ 

$$(\cot^2x)\cot^2x + \cot^2x = 1 \\ \ \\ (\cosec^2x-1)^2+ \cosec^2x - 1 = 1 \\ \ \\ \cosec^4x + 1 -2\cosec^2x + \cosec^2x -1 = 1\\ \ \\ \cosec^4x - \cosec^2x +1-1 = 1\\ \ \\ \cosec^4x - \cosec^2x = 1$$​