Álgebra Ejemplos

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

Paso 1

Simplifica el numerador.

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Paso 1.1

Reescribe $\cot (x)$ en términos de senos y cosenos.

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

Paso 1.2

Factoriza $\cos (x)$ de $\frac{\cos (x)}{\sin (x)} + 2 \cos (x)$ .

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Paso 1.2.1

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

$\frac{\cos (x) \frac{1}{\sin (x)} + 2 \cos (x)}{\csc (x) - \sin (x)}$

Paso 1.2.2

Factoriza $\cos (x)$ de $2 \cos (x)$ .

$\frac{\cos (x) \frac{1}{\sin (x)} + \cos (x) \cdot 2}{\csc (x) - \sin (x)}$

Paso 1.2.3

Factoriza $\cos (x)$ de $\cos (x) \frac{1}{\sin (x)} + \cos (x) \cdot 2$ .

$\frac{\cos (x) (\frac{1}{\sin (x)} + 2)}{\csc (x) - \sin (x)}$

Paso 2

Reescribe $\csc (x)$ en términos de senos y cosenos.

$\frac{\cos (x) (\frac{1}{\sin (x)} + 2)}{\frac{1}{\sin (x)} - \sin (x)}$

Paso 3

Convierte de $\frac{1}{\sin (x)}$ a $\csc (x)$ .

$\frac{\cos (x) (\csc (x) + 2)}{\frac{1}{\sin (x)} - \sin (x)}$

Paso 4

Convierte de $\frac{1}{\sin (x)}$ a $\csc (x)$ .

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