Question

How do you simplify `sin^4 x - cos^4 x`?

Answer 1

`sin^4(x)-cos^4(x)=-cos(2x)`

Explanation:

Using the following

• `a^2-b^2 = (a+b)(a-b)`

• `sin^2(x) + cos^2(x) = 1`

• `cos(2x) = cos^2(x) - sin^2(x)`

We have:

`sin^4(x)-cos^4(x) = (sin^2(x)+cos^2x())(sin^2(x)-cos^2x())`

`=(1)(-cos(2x))`

`=-cos(2x)`