Trigonometrie Beispiele

\tan (3 x)

$\tan (3 x)$

Schritt 1

Wende die Dreifachwinkelfunktion für den Tangens an.

\frac{3 \tan (x) - \tan^{3} (x)}{1 - 3 \tan^{2} (x)}

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

Schritt 2

Faktorisiere

\tan (x)

$\tan (x)$ aus

3 \tan (x) - \tan^{3} (x)

$3 \tan (x) - \tan^{3} (x)$ heraus.

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Schritt 2.1

Faktorisiere

\tan (x)

$\tan (x)$ aus

3 \tan (x)

$3 \tan (x)$ heraus.

\frac{\tan (x) \cdot 3 - \tan^{3} (x)}{1 - 3 \tan^{2} (x)}

$\frac{\tan (x) \cdot 3 - \tan^{3} (x)}{1 - 3 \tan^{2} (x)}$

Schritt 2.2

Faktorisiere

\tan (x)

$\tan (x)$ aus

- \tan^{3} (x)

$- \tan^{3} (x)$ heraus.

\frac{\tan (x) \cdot 3 + \tan (x) (- \tan^{2} (x))}{1 - 3 \tan^{2} (x)}

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

Schritt 2.3

Faktorisiere

\tan (x)

$\tan (x)$ aus

\tan (x) \cdot 3 + \tan (x) (- \tan^{2} (x))

$\tan (x) \cdot 3 + \tan (x) (- \tan^{2} (x))$ heraus.

\frac{\tan (x) (3 - \tan^{2} (x))}{1 - 3 \tan^{2} (x)}

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

\frac{\tan (x) (3 - \tan^{2} (x))}{1 - 3 \tan^{2} (x)}

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

\tan (3 x)

$\tan (3 x)$

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