Trigonometría Ejemplos

$\tan (x) (\sin (x) + \cot (x) \cdot \cos (x))$

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

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

Simplifique cada término.

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

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

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

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

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

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

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

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

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

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

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

Sumar $1$ y $1$ .

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

Aplicar al propiedad distributiva.

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

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

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

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

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

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

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

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

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

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

Sumar $1$ y $1$ .

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

Combina.

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

Simplifique cada término.

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Anula el factor común de $\sin (x)$ .

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Cancele el factor común.

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

Sustituya la expresión.

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

Cancelar el factor común de $\cos^{2} (x)$ y $\cos (x)$ .

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

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

Cancelar los factores comunes.

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Multiplica por $1$ .

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

Cancele el factor común.

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

Sustituya la expresión.

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

Divida $\cos (x)$ entre $1$ .

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

Simplifique cada término.

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

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

Separa fracciones.

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

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

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

Divida $\sin (x)$ entre $1$ .

$\sin (x) \tan (x) + \cos (x)$