How do you factor the expression and use the fundamental identities to simplify $sin^4x-cos^4x$ ?

Question

1348 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-02-15T13:42:24

$=(sinx-cosx)(sinx+cosx)=-cos2x$

Since

$a^2-b^2=(a-b)(a+b)$ ,

it is:

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

$=(sinx-cosx)(sinx+cosx)(sin^2x+cos^2x)$

On the other hand, it's:

$(sin^2x+cos^2x)=1$ ,

then it's

$=(sinx-cosx)(sinx+cosx)=sin^2x-cos^2x$

or

$-cos(2x)$

How do you factor the expression and use the fundamental identities to simplify sin^4x-cos^4xsin^4x-cos^4x?