Trigonometrie Beispiele

$\frac{\sin^{2} (x) - \tan (x)}{\cos^{2} (x) - \cot (x)} = \tan^{2} (x)$

Schritt 1

Beginne auf der linken Seite.

$\frac{\sin^{2} (x) - \tan (x)}{\cos^{2} (x) - \cot (x)}$

Schritt 2

Wandle in Sinus und Kosinus um.

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Schritt 2.1

Schreibe $\tan (x)$ mit Sinus und Kosinus mithilfe der Quotienten-Identitätsgleichung.

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

Schritt 2.2

Schreibe $\cot (x)$ mit Sinus und Kosinus mithilfe der Quotienten-Identitätsgleichung.

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

Schritt 3

Vereinfache.

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Schritt 3.1

Multiply the numerator and denominator of the fraction by $\cos (x) \sin (x)$ .

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Schritt 3.1.1

Mutltipliziere $\frac{{\sin (x)}^{2} - \frac{\sin (x)}{\cos (x)}}{{\cos (x)}^{2} - \frac{\cos (x)}{\sin (x)}}$ mit $\frac{\cos (x) \sin (x)}{\cos (x) \sin (x)}$ .

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

Schritt 3.1.2

Kombinieren.

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

Schritt 3.2

Wende das Distributivgesetz an.

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

Schritt 3.3

Vereinfache durch Kürzen.

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Schritt 3.3.1

Kürze den gemeinsamen Faktor von $\cos (x)$ .

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Schritt 3.3.1.1

Bringe das führende Minuszeichen in $- \frac{\sin (x)}{\cos (x)}$ in den Zähler.

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

Schritt 3.3.1.2

Faktorisiere $\cos (x)$ aus $\cos (x) \sin (x)$ heraus.

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

Schritt 3.3.1.3

Kürze den gemeinsamen Faktor.

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

Schritt 3.3.1.4

Forme den Ausdruck um.

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

Schritt 3.3.2

Potenziere $\sin (x)$ mit $1$ .

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

Schritt 3.3.3

Potenziere $\sin (x)$ mit $1$ .

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

Schritt 3.3.4

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

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

Schritt 3.3.5

Addiere $1$ und $1$ .

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

Schritt 3.3.6

Kürze den gemeinsamen Faktor von $\sin (x)$ .

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Schritt 3.3.6.1

Bringe das führende Minuszeichen in $- \frac{\cos (x)}{\sin (x)}$ in den Zähler.

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

Schritt 3.3.6.2

Kürze den gemeinsamen Faktor.

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

Schritt 3.3.6.3

Forme den Ausdruck um.

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

Schritt 3.3.7

Potenziere $\cos (x)$ mit $1$ .

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

Schritt 3.3.8

Potenziere $\cos (x)$ mit $1$ .

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

Schritt 3.3.9

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

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

Schritt 3.3.10

Addiere $1$ und $1$ .

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

Schritt 3.4

Vereinfache den Zähler.

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Schritt 3.4.1

Faktorisiere ${\sin (x)}^{3}$ aus $\cos (x) \sin (x) {\sin (x)}^{2} - {\sin (x)}^{2}$ heraus.

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Schritt 3.4.1.1

Faktorisiere ${\sin (x)}^{3}$ aus $\cos (x) \sin (x) {\sin (x)}^{2}$ heraus.

$\frac{{\sin (x)}^{3} (\cos (x) \sin (x) {\sin (x)}^{- 1}) - {\sin (x)}^{2}}{\cos (x) \sin (x) {\cos (x)}^{2} - {\cos (x)}^{2}}$

Schritt 3.4.1.2

Faktorisiere ${\sin (x)}^{3}$ aus $- {\sin (x)}^{2}$ heraus.

$\frac{{\sin (x)}^{3} (\cos (x) \sin (x) {\sin (x)}^{- 1}) + {\sin (x)}^{3} (- {\sin (x)}^{- 1})}{\cos (x) \sin (x) {\cos (x)}^{2} - {\cos (x)}^{2}}$

Schritt 3.4.1.3

Faktorisiere ${\sin (x)}^{3}$ aus ${\sin (x)}^{3} (\cos (x) \sin (x) {\sin (x)}^{- 1}) + {\sin (x)}^{3} (- {\sin (x)}^{- 1})$ heraus.

$\frac{{\sin (x)}^{3} (\cos (x) \sin (x) {\sin (x)}^{- 1} - {\sin (x)}^{- 1})}{\cos (x) \sin (x) {\cos (x)}^{2} - {\cos (x)}^{2}}$

Schritt 3.4.2

Faktorisiere ${\sin (x)}^{- 2}$ aus $\cos (x) \sin (x) {\sin (x)}^{- 1} - {\sin (x)}^{- 1}$ heraus.

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Schritt 3.4.2.1

Faktorisiere ${\sin (x)}^{- 2}$ aus $\cos (x) \sin (x) {\sin (x)}^{- 1}$ heraus.

$\frac{{\sin (x)}^{3} ({\sin (x)}^{- 2} (\cos (x) \sin (x) \sin (x)) - {\sin (x)}^{- 1})}{\cos (x) \sin (x) {\cos (x)}^{2} - {\cos (x)}^{2}}$

Schritt 3.4.2.2

Faktorisiere ${\sin (x)}^{- 2}$ aus $- {\sin (x)}^{- 1}$ heraus.

$\frac{{\sin (x)}^{3} ({\sin (x)}^{- 2} (\cos (x) \sin (x) \sin (x)) + {\sin (x)}^{- 2} (- \sin (x)))}{\cos (x) \sin (x) {\cos (x)}^{2} - {\cos (x)}^{2}}$

Schritt 3.4.2.3

Faktorisiere ${\sin (x)}^{- 2}$ aus ${\sin (x)}^{- 2} (\cos (x) \sin (x) \sin (x)) + {\sin (x)}^{- 2} (- \sin (x))$ heraus.

$\frac{{\sin (x)}^{3} ({\sin (x)}^{- 2} (\cos (x) \sin (x) \sin (x) - \sin (x)))}{\cos (x) \sin (x) {\cos (x)}^{2} - {\cos (x)}^{2}}$

Schritt 3.4.3

Multipliziere $\cos (x) \sin (x) \sin (x)$ .

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Schritt 3.4.3.1

Potenziere $\sin (x)$ mit $1$ .

$\frac{{\sin (x)}^{3} ({\sin (x)}^{- 2} (\cos (x) ({\sin (x)}^{1} \sin (x)) - \sin (x)))}{\cos (x) \sin (x) {\cos (x)}^{2} - {\cos (x)}^{2}}$

Schritt 3.4.3.2

Potenziere $\sin (x)$ mit $1$ .

$\frac{{\sin (x)}^{3} ({\sin (x)}^{- 2} (\cos (x) ({\sin (x)}^{1} {\sin (x)}^{1}) - \sin (x)))}{\cos (x) \sin (x) {\cos (x)}^{2} - {\cos (x)}^{2}}$

Schritt 3.4.3.3

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

$\frac{{\sin (x)}^{3} ({\sin (x)}^{- 2} (\cos (x) {\sin (x)}^{1 + 1} - \sin (x)))}{\cos (x) \sin (x) {\cos (x)}^{2} - {\cos (x)}^{2}}$

Schritt 3.4.3.4

Addiere $1$ und $1$ .

$\frac{{\sin (x)}^{3} ({\sin (x)}^{- 2} (\cos (x) {\sin (x)}^{2} - \sin (x)))}{\cos (x) \sin (x) {\cos (x)}^{2} - {\cos (x)}^{2}}$

Schritt 3.4.4

Faktorisiere $\sin (x)$ aus $\cos (x) {\sin (x)}^{2} - \sin (x)$ heraus.

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Schritt 3.4.4.1

Faktorisiere $\sin (x)$ aus $\cos (x) {\sin (x)}^{2}$ heraus.

$\frac{{\sin (x)}^{3} ({\sin (x)}^{- 2} (\sin (x) (\cos (x) \sin (x)) - \sin (x)))}{\cos (x) \sin (x) {\cos (x)}^{2} - {\cos (x)}^{2}}$

Schritt 3.4.4.2

Faktorisiere $\sin (x)$ aus $- \sin (x)$ heraus.

$\frac{{\sin (x)}^{3} ({\sin (x)}^{- 2} (\sin (x) (\cos (x) \sin (x)) + \sin (x) \cdot - 1))}{\cos (x) \sin (x) {\cos (x)}^{2} - {\cos (x)}^{2}}$

Schritt 3.4.4.3

Faktorisiere $\sin (x)$ aus $\sin (x) (\cos (x) \sin (x)) + \sin (x) \cdot - 1$ heraus.

$\frac{{\sin (x)}^{3} ({\sin (x)}^{- 2} (\sin (x) (\cos (x) \sin (x) - 1)))}{\cos (x) \sin (x) {\cos (x)}^{2} - {\cos (x)}^{2}}$

$\frac{{\sin (x)}^{3} ({\sin (x)}^{- 2} \sin (x) (\cos (x) \sin (x) - 1))}{\cos (x) \sin (x) {\cos (x)}^{2} - {\cos (x)}^{2}}$

Schritt 3.4.5

Multipliziere ${\sin (x)}^{- 2}$ mit $\sin (x)$ durch Addieren der Exponenten.

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Schritt 3.4.5.1

Mutltipliziere ${\sin (x)}^{- 2}$ mit $\sin (x)$ .

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Schritt 3.4.5.1.1

Potenziere $\sin (x)$ mit $1$ .

$\frac{{\sin (x)}^{3} ({\sin (x)}^{- 2} {\sin (x)}^{1} (\cos (x) \sin (x) - 1))}{\cos (x) \sin (x) {\cos (x)}^{2} - {\cos (x)}^{2}}$

Schritt 3.4.5.1.2

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

$\frac{{\sin (x)}^{3} ({\sin (x)}^{- 2 + 1} (\cos (x) \sin (x) - 1))}{\cos (x) \sin (x) {\cos (x)}^{2} - {\cos (x)}^{2}}$

Schritt 3.4.5.2

Addiere $- 2$ und $1$ .

$\frac{{\sin (x)}^{3} ({\sin (x)}^{- 1} (\cos (x) \sin (x) - 1))}{\cos (x) \sin (x) {\cos (x)}^{2} - {\cos (x)}^{2}}$

$\frac{{\sin (x)}^{3} {\sin (x)}^{- 1} (\cos (x) \sin (x) - 1)}{\cos (x) \sin (x) {\cos (x)}^{2} - {\cos (x)}^{2}}$

Schritt 3.4.6

Multipliziere ${\sin (x)}^{3}$ mit ${\sin (x)}^{- 1}$ durch Addieren der Exponenten.

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Schritt 3.4.6.1

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

$\frac{{\sin (x)}^{3 - 1} (\cos (x) \sin (x) - 1)}{\cos (x) \sin (x) {\cos (x)}^{2} - {\cos (x)}^{2}}$

Schritt 3.4.6.2

Subtrahiere $1$ von $3$ .

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

Schritt 3.5

Vereinfache den Nenner.

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Schritt 3.5.1

Faktorisiere ${\cos (x)}^{3}$ aus $\cos (x) \sin (x) {\cos (x)}^{2} - {\cos (x)}^{2}$ heraus.

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Schritt 3.5.1.1

Faktorisiere ${\cos (x)}^{3}$ aus $\cos (x) \sin (x) {\cos (x)}^{2}$ heraus.

$\frac{{\sin (x)}^{2} (\cos (x) \sin (x) - 1)}{{\cos (x)}^{3} (\cos (x) \sin (x) {\cos (x)}^{- 1}) - {\cos (x)}^{2}}$

Schritt 3.5.1.2

Faktorisiere ${\cos (x)}^{3}$ aus $- {\cos (x)}^{2}$ heraus.

$\frac{{\sin (x)}^{2} (\cos (x) \sin (x) - 1)}{{\cos (x)}^{3} (\cos (x) \sin (x) {\cos (x)}^{- 1}) + {\cos (x)}^{3} (- {\cos (x)}^{- 1})}$

Schritt 3.5.1.3

Faktorisiere ${\cos (x)}^{3}$ aus ${\cos (x)}^{3} (\cos (x) \sin (x) {\cos (x)}^{- 1}) + {\cos (x)}^{3} (- {\cos (x)}^{- 1})$ heraus.

$\frac{{\sin (x)}^{2} (\cos (x) \sin (x) - 1)}{{\cos (x)}^{3} (\cos (x) \sin (x) {\cos (x)}^{- 1} - {\cos (x)}^{- 1})}$

Schritt 3.5.2

Faktorisiere ${\cos (x)}^{- 2}$ aus $\cos (x) \sin (x) {\cos (x)}^{- 1} - {\cos (x)}^{- 1}$ heraus.

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Schritt 3.5.2.1

Faktorisiere ${\cos (x)}^{- 2}$ aus $\cos (x) \sin (x) {\cos (x)}^{- 1}$ heraus.

$\frac{{\sin (x)}^{2} (\cos (x) \sin (x) - 1)}{{\cos (x)}^{3} ({\cos (x)}^{- 2} (\cos (x) \sin (x) \cos (x)) - {\cos (x)}^{- 1})}$

Schritt 3.5.2.2

Faktorisiere ${\cos (x)}^{- 2}$ aus $- {\cos (x)}^{- 1}$ heraus.

$\frac{{\sin (x)}^{2} (\cos (x) \sin (x) - 1)}{{\cos (x)}^{3} ({\cos (x)}^{- 2} (\cos (x) \sin (x) \cos (x)) + {\cos (x)}^{- 2} (- \cos (x)))}$

Schritt 3.5.2.3

Faktorisiere ${\cos (x)}^{- 2}$ aus ${\cos (x)}^{- 2} (\cos (x) \sin (x) \cos (x)) + {\cos (x)}^{- 2} (- \cos (x))$ heraus.

$\frac{{\sin (x)}^{2} (\cos (x) \sin (x) - 1)}{{\cos (x)}^{3} ({\cos (x)}^{- 2} (\cos (x) \sin (x) \cos (x) - \cos (x)))}$

Schritt 3.5.3

Multipliziere $\cos (x) \sin (x) \cos (x)$ .

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Schritt 3.5.3.1

Potenziere $\cos (x)$ mit $1$ .

$\frac{{\sin (x)}^{2} (\cos (x) \sin (x) - 1)}{{\cos (x)}^{3} ({\cos (x)}^{- 2} ({\cos (x)}^{1} \cos (x) \sin (x) - \cos (x)))}$

Schritt 3.5.3.2

Potenziere $\cos (x)$ mit $1$ .

$\frac{{\sin (x)}^{2} (\cos (x) \sin (x) - 1)}{{\cos (x)}^{3} ({\cos (x)}^{- 2} ({\cos (x)}^{1} {\cos (x)}^{1} \sin (x) - \cos (x)))}$

Schritt 3.5.3.3

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

$\frac{{\sin (x)}^{2} (\cos (x) \sin (x) - 1)}{{\cos (x)}^{3} ({\cos (x)}^{- 2} ({\cos (x)}^{1 + 1} \sin (x) - \cos (x)))}$

Schritt 3.5.3.4

Addiere $1$ und $1$ .

$\frac{{\sin (x)}^{2} (\cos (x) \sin (x) - 1)}{{\cos (x)}^{3} ({\cos (x)}^{- 2} ({\cos (x)}^{2} \sin (x) - \cos (x)))}$

Schritt 3.5.4

Faktorisiere $\cos (x)$ aus ${\cos (x)}^{2} \sin (x) - \cos (x)$ heraus.

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Schritt 3.5.4.1

Faktorisiere $\cos (x)$ aus ${\cos (x)}^{2} \sin (x)$ heraus.

$\frac{{\sin (x)}^{2} (\cos (x) \sin (x) - 1)}{{\cos (x)}^{3} ({\cos (x)}^{- 2} (\cos (x) (\cos (x) \sin (x)) - \cos (x)))}$

Schritt 3.5.4.2

Faktorisiere $\cos (x)$ aus $- \cos (x)$ heraus.

$\frac{{\sin (x)}^{2} (\cos (x) \sin (x) - 1)}{{\cos (x)}^{3} ({\cos (x)}^{- 2} (\cos (x) (\cos (x) \sin (x)) + \cos (x) \cdot - 1))}$

Schritt 3.5.4.3

Faktorisiere $\cos (x)$ aus $\cos (x) (\cos (x) \sin (x)) + \cos (x) \cdot - 1$ heraus.

$\frac{{\sin (x)}^{2} (\cos (x) \sin (x) - 1)}{{\cos (x)}^{3} ({\cos (x)}^{- 2} (\cos (x) (\cos (x) \sin (x) - 1)))}$

$\frac{{\sin (x)}^{2} (\cos (x) \sin (x) - 1)}{{\cos (x)}^{3} ({\cos (x)}^{- 2} \cos (x) (\cos (x) \sin (x) - 1))}$

Schritt 3.5.5

Multipliziere ${\cos (x)}^{- 2}$ mit $\cos (x)$ durch Addieren der Exponenten.

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Schritt 3.5.5.1

Mutltipliziere ${\cos (x)}^{- 2}$ mit $\cos (x)$ .

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Schritt 3.5.5.1.1

Potenziere $\cos (x)$ mit $1$ .

$\frac{{\sin (x)}^{2} (\cos (x) \sin (x) - 1)}{{\cos (x)}^{3} ({\cos (x)}^{- 2} {\cos (x)}^{1} (\cos (x) \sin (x) - 1))}$

Schritt 3.5.5.1.2

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

$\frac{{\sin (x)}^{2} (\cos (x) \sin (x) - 1)}{{\cos (x)}^{3} ({\cos (x)}^{- 2 + 1} (\cos (x) \sin (x) - 1))}$

Schritt 3.5.5.2

Addiere $- 2$ und $1$ .

$\frac{{\sin (x)}^{2} (\cos (x) \sin (x) - 1)}{{\cos (x)}^{3} ({\cos (x)}^{- 1} (\cos (x) \sin (x) - 1))}$

$\frac{{\sin (x)}^{2} (\cos (x) \sin (x) - 1)}{{\cos (x)}^{3} {\cos (x)}^{- 1} (\cos (x) \sin (x) - 1)}$

Schritt 3.5.6

Multipliziere ${\cos (x)}^{3}$ mit ${\cos (x)}^{- 1}$ durch Addieren der Exponenten.

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Schritt 3.5.6.1

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

$\frac{{\sin (x)}^{2} (\cos (x) \sin (x) - 1)}{{\cos (x)}^{3 - 1} (\cos (x) \sin (x) - 1)}$

Schritt 3.5.6.2

Subtrahiere $1$ von $3$ .

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

Schritt 3.6

Kürze den gemeinsamen Faktor von $\cos (x) \sin (x) - 1$ .

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

Schritt 4

Schreibe $\frac{\sin^{2} (x)}{\cos^{2} (x)}$ als $\tan^{2} (x)$ um.

$\tan^{2} (x)$

Schritt 5

Da gezeigt wurde, dass die beiden Seiten äquivalent sind, ist die Gleichung eine Identitätsgleichung.

$\frac{\sin^{2} (x) - \tan (x)}{\cos^{2} (x) - \cot (x)} = \tan^{2} (x)$ ist eine Identitätsgleichung