Algebra Esempi

\frac{\csc (x) \cos (x)}{\tan (x) + \cot (x)}

$\frac{\csc (x) \cos (x)}{\tan (x) + \cot (x)}$

Passaggio 1

Riscrivi

\csc (x)

$\csc (x)$ in termini di seno e coseno.

\frac{\frac{1}{\sin (x)} \cos (x)}{\tan (x) + \cot (x)}

$\frac{\frac{1}{\sin (x)} \cos (x)}{\tan (x) + \cot (x)}$

Passaggio 2

Semplifica il denominatore.

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Passaggio 2.1

Riscrivi

\tan (x)

$\tan (x)$ in termini di seno e coseno.

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

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

Passaggio 2.2

Riscrivi

\cot (x)

$\cot (x)$ in termini di seno e coseno.

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

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

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

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

Passaggio 3

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

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

\cos (x)

$\cos (x)$ .

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

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

Passaggio 4

Moltiplica il numeratore per il reciproco del denominatore.

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

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

Passaggio 5

Moltiplica

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

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

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

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

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

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

Passaggio 6

Frazioni separate.

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

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

Passaggio 7

Converti da

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

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

\cot (x)

$\cot (x)$ .

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

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

Passaggio 8

Semplifica ciascun termine.

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Passaggio 8.1

Converti da

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

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

\tan (x)

$\tan (x)$ .

\frac{1}{\tan (x) + \frac{\cos (x)}{\sin (x)}} \cot (x)

$\frac{1}{\tan (x) + \frac{\cos (x)}{\sin (x)}} \cot (x)$

Passaggio 8.2

Converti da

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

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

\cot (x)

$\cot (x)$ .

\frac{1}{\tan (x) + \cot (x)} \cot (x)

$\frac{1}{\tan (x) + \cot (x)} \cot (x)$

\frac{1}{\tan (x) + \cot (x)} \cot (x)

$\frac{1}{\tan (x) + \cot (x)} \cot (x)$

Passaggio 9

\frac{1}{\tan (x) + \cot (x)}

$\frac{1}{\tan (x) + \cot (x)}$ e

\cot (x)

$\cot (x)$ .

\frac{\cot (x)}{\tan (x) + \cot (x)}

$\frac{\cot (x)}{\tan (x) + \cot (x)}$