Elementarmathematik Beispiele

\frac{\csc (x) \sin (x)}{\cot (x)}

$\frac{\csc (x) \sin (x)}{\cot (x)}$

Schritt 1

Separiere Brüche.

\frac{\sin (x)}{1} \cdot \frac{\csc (x)}{\cot (x)}

$\frac{\sin (x)}{1} \cdot \frac{\csc (x)}{\cot (x)}$

Schritt 2

Schreibe

\cot (x)

$\cot (x)$ mithilfe von Sinus und Kosinus um.

\frac{\sin (x)}{1} \cdot \frac{\csc (x)}{\frac{\cos (x)}{\sin (x)}}

$\frac{\sin (x)}{1} \cdot \frac{\csc (x)}{\frac{\cos (x)}{\sin (x)}}$

Schritt 3

Schreibe

\csc (x)

$\csc (x)$ mithilfe von Sinus und Kosinus um.

\frac{\sin (x)}{1} \cdot \frac{\frac{1}{\sin (x)}}{\frac{\cos (x)}{\sin (x)}}

$\frac{\sin (x)}{1} \cdot \frac{\frac{1}{\sin (x)}}{\frac{\cos (x)}{\sin (x)}}$

Schritt 4

Multipliziere mit dem Kehrwert des Bruchs, um durch

\frac{\cos (x)}{\sin (x)}

$\frac{\cos (x)}{\sin (x)}$ zu dividieren.

\frac{\sin (x)}{1} (\frac{1}{\sin (x)} \cdot \frac{\sin (x)}{\cos (x)})

$\frac{\sin (x)}{1} (\frac{1}{\sin (x)} \cdot \frac{\sin (x)}{\cos (x)})$

Schritt 5

Kürze den gemeinsamen Faktor von

\sin (x)

$\sin (x)$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 5.1

Kürze den gemeinsamen Faktor.

\frac{\sin (x)}{1} (\frac{1}{\sin (x)} \cdot \frac{\sin (x)}{\cos (x)})

$\frac{\sin (x)}{1} (\frac{1}{\sin (x)} \cdot \frac{\sin (x)}{\cos (x)})$

Schritt 5.2

Forme den Ausdruck um.

\frac{\sin (x)}{1} \cdot \frac{1}{\cos (x)}

$\frac{\sin (x)}{1} \cdot \frac{1}{\cos (x)}$

\frac{\sin (x)}{1} \cdot \frac{1}{\cos (x)}

$\frac{\sin (x)}{1} \cdot \frac{1}{\cos (x)}$

Schritt 6

Dividiere

\sin (x)

$\sin (x)$ durch

1

$1$ .

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

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

Schritt 7

Kombiniere

\sin (x)

$\sin (x)$ und

\frac{1}{\cos (x)}

$\frac{1}{\cos (x)}$ .

\frac{\sin (x)}{\cos (x)}

$\frac{\sin (x)}{\cos (x)}$

Schritt 8

Wandle von

\frac{\sin (x)}{\cos (x)}

$\frac{\sin (x)}{\cos (x)}$ nach

\tan (x)

$\tan (x)$ um.

\tan (x)

$\tan (x)$