[tex]\bf sin^2(\theta)+cos^2(\theta)=1
\\\\\\
\textit{difference of squares}
\\ \quad \\
(a-b)(a+b) = a^2-b^2\qquad \qquad
a^2-b^2 = (a-b)(a+b)\\\\
-----------------------------\\\\
\cfrac{sin^4(x)-cos^4(x)}{sin^2(x)-cos^2(x)}=1\\\\
-----------------------------\\\\[/tex]
[tex]\bf \cfrac{sin^4(x)-cos^4(x)}{sin^2(x)-cos^2(x)}\implies \cfrac{[sin^2(x)-cos^2(x)][sin^2(x)+cos^2(x)]}{sin^2(x)-cos^2(x)}
\\\\\\
\cfrac{[sin^2(x)+cos^2(x)]}{1}\implies \cfrac{1}{1}\implies 1[/tex]
