Trigonometría Ejemplos

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

Step 1

Factoriza $1$ de $\frac{\cot^{2} (x)}{1 - \sin^{2} (x)} + \frac{\tan^{2} (x)}{1 - \cos^{2} (x)}$ .

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Factoriza $1$ de $\frac{\cot^{2} (x)}{1 - \sin^{2} (x)}$ .

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

Factoriza $1$ de $\frac{\tan^{2} (x)}{1 - \cos^{2} (x)}$ .

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

Factoriza $1$ de $1 \frac{\cot^{2} (x)}{1 - \sin^{2} (x)} + 1 \frac{\tan^{2} (x)}{1 - \cos^{2} (x)}$ .

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

Step 2

Aplica la identidad pitagórica.

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

Step 3

Aplica la identidad pitagórica.

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

Step 4

Simplifica los términos.

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

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

Simplifica cada término.

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Reescribe $\frac{\cot^{2} (x)}{\cos^{2} (x)}$ como ${(\frac{\cot (x)}{\cos (x)})}^{2}$ .

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

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

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

Reescribe $\frac{\frac{\cos (x)}{\sin (x)}}{\cos (x)}$ como un producto.

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

Cancela el factor común de $\cos (x)$ .

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Cancela el factor común.

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

Reescribe la expresión.

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

Aplica la regla del producto a $\frac{1}{\sin (x)}$ .

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

Uno elevado a cualquier potencia es uno.

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

Reescribe $\frac{\tan^{2} (x)}{\sin^{2} (x)}$ como ${(\frac{\tan (x)}{\sin (x)})}^{2}$ .

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

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

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

Reescribe $\frac{\frac{\sin (x)}{\cos (x)}}{\sin (x)}$ como un producto.

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

Cancela el factor común de $\sin (x)$ .

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Cancela el factor común.

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

Reescribe la expresión.

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

Aplica la regla del producto a $\frac{1}{\cos (x)}$ .

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

Uno elevado a cualquier potencia es uno.

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

Simplifica cada término.

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Reescribe $1$ como $1^{2}$ .

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

Reescribe $\frac{1^{2}}{\sin^{2} (x)}$ como ${(\frac{1}{\sin (x)})}^{2}$ .

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

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

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

Reescribe $1$ como $1^{2}$ .

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

Reescribe $\frac{1^{2}}{\cos^{2} (x)}$ como ${(\frac{1}{\cos (x)})}^{2}$ .

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

Convierte de $\frac{1}{\cos (x)}$ a $\sec (x)$ .

$\csc^{2} (x) + \sec^{2} (x)$