Correct Answer: 1

Solution : Given: $\sin^4x + \sin^2x = 1$
⇒ $\sin^4x = 1 – \sin^2x$
By using the trigonometric identity: $\cos^2x=1-\sin^2x$
⇒ $\sin^4x = \cos^2x$
Dividing both sides by $\sin^2x$
⇒ $\frac{\sin^4x}{\sin^2x} = \frac{\cos^2x}{\sin^2x}$
⇒ $\sin^2x = \cot^2x$..................(1)
$\therefore \sin^4x = \cot^4x$..............(2)
So, $\cot^4x+ \cot^2x= \sin^4x + \sin^2x =1$
Hence, the correct answer is 1.