Aljabar Contoh

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

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

Langkah 1

Tulis kembali

csc (x)

$\csc (x)$ dalam bentuk sinus dan kosinus.

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

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

Langkah 2

Sederhanakan penyebutnya.

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Langkah 2.1

Tulis kembali

tan (x)

$\tan (x)$ dalam bentuk sinus dan kosinus.

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

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

Langkah 2.2

Tulis kembali

cot (x)

$\cot (x)$ dalam bentuk sinus dan kosinus.

\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)}}

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

Langkah 3

Gabungkan

\frac{1}{sin (x)}

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

cos (x)

$\cos (x)$ .

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

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

Langkah 4

Kalikan pembilang dengan balikan dari penyebut.

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

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

Langkah 5

Kalikan

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

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

\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)})}

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

Langkah 6

Pisahkan pecahan.

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

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

Langkah 7

Konversikan dari

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

$\cot (x)$ .

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

Langkah 8

Sederhanakan setiap suku.

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Langkah 8.1

Konversikan dari

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

$\tan (x)$ .

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

Langkah 8.2

Konversikan dari

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

$\cot (x)$ .

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

Langkah 9

Gabungkan

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

$\cot (x)$ .

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