Trigonometría Ejemplos

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

Step 1

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

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

Step 2

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

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

Step 3

Combina $\frac{1}{\sin (x)}$ y $\cos^{2} (x)$ .

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

Step 4

Multiplica el numerador por la recíproca del denominador.

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

Step 5

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

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

Step 6

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

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

Step 7

Separa las fracciones.

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

Step 8

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

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

Step 9

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

$\frac{\cos (x)}{1 + \csc (x)} \cot (x)$

Step 10

Combina $\frac{\cos (x)}{1 + \csc (x)}$ y $\cot (x)$ .

$\frac{\cos (x) \cot (x)}{1 + \csc (x)}$