Trigonometría Ejemplos

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

Step 1

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

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

Step 2

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

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

Step 3

Simplifica el numerador.

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Eleva $\cos (x)$ a la potencia de $1$ .

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

Eleva $\cos (x)$ a la potencia de $1$ .

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

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

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

Suma $1$ y $1$ .

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

Step 4

Multiplica el numerador por la recíproca del denominador.

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

Step 5

Multiplica $\frac{\cos^{2} (x)}{\sin (x)}$ por $\frac{1}{1 - \sin (x)}$ .

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

Step 6

Factoriza $\cos (x)$ de $\cos^{2} (x)$ .

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

Step 7

Separa las fracciones.

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

Step 8

Convierte de $\frac{\cos (x)}{\sin (x)}$ a $\cot (x)$ .

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

Step 9

Combina $\frac{\cos (x)}{1 - \sin (x)}$ y $\cot (x)$ .

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