Trigonometría Ejemplos

$\cot (x) \csc (x) (1 - \cos (x))$

Step 1

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

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

Step 2

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

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

Step 3

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

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

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

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

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

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

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

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

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

Suma $1$ y $1$ .

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

Step 4

Aplica la propiedad distributiva.

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

Step 5

Simplifica la expresión.

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

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

Reescribe con la propiedad conmutativa de la multiplicación.

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

Step 6

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

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Combina $\cos (x)$ y $\frac{\cos (x)}{\sin^{2} (x)}$ .

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

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

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

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

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

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

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

Suma $1$ y $1$ .

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

Step 7

Simplifica cada término.

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

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

Separa las fracciones.

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

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

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

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

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

Convierte de $\frac{\cos^{2} (x)}{\sin^{2} (x)}$ a $\cot^{2} (x)$ .

$\csc (x) \cot (x) - \cot^{2} (x)$