Question

How do you verify `cos^4 x - sin^4 x = cos^2 x - sin^2 x`?

Answer 1

`cos^4x` - `sin^4x`
`(cos^2x)^2 - (sin^2)^2`
`(cos^2x+ sin^2x)(cos^2x - sin^2x)` --applying the formula of `a^2 - b^2`
`1 × (cos^2x - sin^2x)` --- since `cos^2x+sin^2x` =1
`cos^2x - sin^2x`