Trigonometrie Beispiele

\frac{1 - (cos (x) + sin (x)) (cos (x) + sin (x))}{sin (x) cos (x)}

$\frac{1 - (\cos (x) + \sin (x)) (\cos (x) + \sin (x))}{\sin (x) \cos (x)}$

Schritt 1

Schreibe

$1$ als

$1^{2}$ um.

$\frac{1^{2} - (\cos (x) + \sin (x)) (\cos (x) + \sin (x))}{\sin (x) \cos (x)}$

Schritt 2

Schreibe

$(\cos (x) + \sin (x)) (\cos (x) + \sin (x))$ als

${(\cos (x) + \sin (x))}^{2}$ um.

$\frac{1^{2} - {(\cos (x) + \sin (x))}^{2}}{\sin (x) \cos (x)}$

Schritt 3

Da beide Terme perfekte Quadrate sind, faktorisiere durch Anwendung der dritten binomischen Formel,

$a^{2} - b^{2} = (a + b) (a - b)$ , mit

$a = 1$ und

$b = \cos (x) + \sin (x)$ .

$\frac{(1 + \cos (x) + \sin (x)) (1 - (\cos (x) + \sin (x)))}{\sin (x) \cos (x)}$

Schritt 4

Wende das Distributivgesetz an.

$\frac{(1 + \cos (x) + \sin (x)) (1 - \cos (x) - \sin (x))}{\sin (x) \cos (x)}$