Precálculo Ejemplos

$\frac{\cot (t)}{\csc (t) - \sin (t)}$

Paso 1

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

$\frac{\frac{\cos (t)}{\sin (t)}}{\csc (t) - \sin (t)}$

Paso 2

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

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

Paso 3

Multiplica el numerador por la recíproca del denominador.

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

Paso 4

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

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

Paso 5

Separa las fracciones.

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

Paso 6

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

$\frac{1}{\frac{1}{\sin (t)} - \sin (t)} \cot (t)$

Paso 7

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

$\frac{1}{\csc (t) - \sin (t)} \cot (t)$

Paso 8

Combina $\frac{1}{\csc (t) - \sin (t)}$ y $\cot (t)$ .

$\frac{\cot (t)}{\csc (t) - \sin (t)}$