Question

How do you verify `sin^4x-cos^4x=1-2cos^2x`?

Answer 1

See Below

Explanation:

`LHS:`
`sin^4 x -cos^4 x =(sin^2x-cos^2x) (sin^2x+cos^2x)`->factor

`=(sin^2x-cos^2x)*1`

`=(1-cos^2x)-cos^2x`->use the property `sin^2x+cos^2x=1`

`=1-2cos^2x`

`=RHS`