Forme $(1-{\displaystyle \frac{1}{\cos (x)}})(1+{\displaystyle \frac{1}{\cos (x)}})\backslash left(1-\backslash dfrac\{1\}\{\backslash cos(x)\}\backslash right)\backslash left(1+\backslash dfrac\{1\}\{\backslash cos(x)\}\backslash right)$ um.

Verwende die dritte binomische Formel.

$=1-{\displaystyle \frac{1}{{\cos }^2(x)}}=\; 1-\backslash dfrac\{1\}\{\backslash cos^2(x)\}$

Bilde den Hauptnenner und führe die Brüche zusammen.

$={\displaystyle \frac{{\cos }^2(x)-1}{{\cos }^2(x)}}=\backslash dfrac\{\backslash cos^2(x)-1\}\{\backslash cos^2(x)\}$

Verwende den trigonometrischen Pythagoras.

$=-{\displaystyle \frac{{\sin }^2(x)}{{\cos }^2(x)}}=-\backslash dfrac\{\backslash sin^2(x)\}\{\backslash cos^2(x)\}$

Verwende die Definition des Tangens.

$=-(\tan (x){)}^2=-(\backslash tan(x))^2$