Question

If cot^(4)x − cot^(2)x = 1, then the value of cos^(4)x + cos^(2)x is

Answer 1

1

Explanation:

`cot^4x-cot^2x=1\\cot^4x=1+cot^2x\\cot^4x=cosec^2x\\ cos^4xsin^2x=sin^4x\\cos^4x=(sin^4x)/(sin^2x)\\cos^4x=sin^2x`------- (1)

Putting the value of
`cos^4x` in the equation:

`cos^4x+cos^2x\\sin ^2x +cos^2x\\1` (Using the identity
`cos^2x +sin^2x=1)`