حساب المثلثات الأمثلة

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

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

خطوة 1

بسّط بَسْط الكسر.

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خطوة 1.1

أعِد كتابة

csc (x)

$\csc (x)$ من حيث الجيوب وجيوب التمام.

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

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

خطوة 1.2

أعِد كتابة

cot (x)

$\cot (x)$ من حيث الجيوب وجيوب التمام.

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

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

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

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

خطوة 2

بسّط القاسم.

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خطوة 2.1

أعِد كتابة

tan (x)

$\tan (x)$ من حيث الجيوب وجيوب التمام.

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

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

خطوة 2.2

أخرِج العامل

sin (x)

$\sin (x)$ من

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

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

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خطوة 2.2.1

أخرِج العامل

sin (x)

$\sin (x)$ من

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

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

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

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

خطوة 2.2.2

اضرب في

1

$1$ .

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

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

خطوة 2.2.3

أخرِج العامل

sin (x)

$\sin (x)$ من

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

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

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

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

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

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

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

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

خطوة 3

بسّط كل حد.

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خطوة 3.1

حوّل من

\frac{1}{sin (x)}

$\frac{1}{\sin (x)}$ إلى

csc (x)

$\csc (x)$ .

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

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

خطوة 3.2

حوّل من

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

$\frac{\cos (x)}{\sin (x)}$ إلى

cot (x)

$\cot (x)$ .

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

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

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

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

خطوة 4

حوّل من

\frac{1}{cos (x)}

$\frac{1}{\cos (x)}$ إلى

sec (x)

$\sec (x)$ .

\frac{csc (x) + cot (x)}{sin (x) (sec (x) + 1)}

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