If sin^4x + sin^2x = 1, then what is the value of cot^4x + cot^2x ?

We are given that,

 $sin^4x + sin^2x = 1$

 $sin^4x  = 1 - sin^2x$

{ we know, sin²x + cos²x = 1 }

 $sin^4x  = cos^2x$

sin²x = \(\frac{cos²x}{sin²x}\)

sin²x = cot²x    -----(1)

Now,

$cot^4x + cot^2x$

By using equation 1.

= sin⁴ x + sin²x 

= 1          { given }