Question

How do you prove `(cos^4x - sin^4x)/sin^2x=cot^2x-1`?

Answer 1

Prove trig equation.

Explanation:

`cos^4 x - sin^2 x = (cos ^2 x - sin^2 x( (cos^2 x + sin^2 x) =`
`= (cos@ x - sin^2 x).` because (cos^2 x + sin^2 x) = 1
`(cos^2 x - sin^2 x)/(sin^2 x) = cos^2 x/(sin^2 x) - sin^2 x/(sin^2 x) =`
`= cot^2 x - 1`