Algebra Beispiele

\frac{cot (x) - tan (x)}{sin (x) cos (x)}

$\frac{\cot (x) - \tan (x)}{\sin (x) \cos (x)}$

Schritt 1

Vereinfache den Zähler.

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Schritt 1.1

Schreibe

cot (x)

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

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

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

Schritt 1.2

Schreibe

tan (x)

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

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

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

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

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

Schritt 2

Vereinfache den Zähler.

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Schritt 2.1

Wandle von

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

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

tan (x)

$\tan (x)$ um.

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

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

Schritt 2.2

Wandle von

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

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

cot (x)

$\cot (x)$ um.

\frac{cot (x) - tan (x)}{sin (x) cos (x)}

$\frac{\cot (x) - \tan (x)}{\sin (x) \cos (x)}$

\frac{cot (x) - tan (x)}{sin (x) cos (x)}

$\frac{\cot (x) - \tan (x)}{\sin (x) \cos (x)}$