​$$\text{If } \cot^4 A + \cot^2 A = 1, \text{ then find the value of } \cos^4 A - 3 \cos^2 A.$$​​

Correct option is A

Given:

​$$\cot^4 A + \cot^2 A = 1$$

Solution:

$$\cot^2 A \left( \cot^2 A + 1 \right) = 1\\\frac{\cos^2 A}{\sin^2 A} \times \frac{1}{\sin^2 A} = 1\\\ \\ \cos^2 A = \sin^4 A$$  

$$\cos^2 A = (1 - \cos^2 A)^2\\\cos^2 A = 1 + \cos^4 A - 2\cos^2 A\\-1 = \cos^4 A - 3\cos^2 A\\$$​