Given:
We need to solve
[tex]\cos ^4x-\sin ^4x[/tex]
Solution;
Now,
[tex]\begin{gathered} \cos ^4x-\sin ^4x=(\cos ^2x)^2-(\sin ^2x)^2 \\ =(\cos ^2x-\sin ^2x)(\cos ^2x+\sin ^2x) \\ =(\cos 2x)(1) \\ =\cos 2x \end{gathered}[/tex]
So,the simpler form is
[tex]\cos 2x[/tex]
