Trigonometrie Beispiele

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

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

Schritt 1

Vereinfache jeden Term.

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Schritt 1.1

Schreibe mithilfe von Sinus und Kosinus um, kürze dann die gemeinsamen Faktoren.

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Schritt 1.1.1

Füge Klammern hinzu.

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

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

Schritt 1.1.2

Stelle

\sin (x)

$\sin (x)$ und

\cot (x)

$\cot (x)$ um.

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

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

Schritt 1.1.3

Schreibe

2 \sin (x) \cot (x)

$2 \sin (x) \cot (x)$ mithilfe von Sinus und Kosinus um.

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

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

Schritt 1.1.4

Kürze die gemeinsamen Faktoren.

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

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

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

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

Schritt 1.2

Schreibe

\cot (x)

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

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

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

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

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

Schritt 2

Wandle von

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

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

\cot (x)

$\cot (x)$ um.

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

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