Trigonometría Ejemplos

\cot (\frac{π}{2} - x) \cos (x)

$\cot (\frac{π}{2} - x) \cos (x)$

Step 1

Aplica la diferencia de la razón de los ángulos.

\frac{\cot (\frac{π}{2}) \cot (x) + 1}{\cot (x) - \cot (\frac{π}{2})} \cos (x)

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

Step 2

Simplifica el numerador.

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El valor exacto de

\cot (\frac{π}{2})

$\cot (\frac{π}{2})$ es

0

$0$ .

\frac{0 \cot (x) + 1}{\cot (x) - \cot (\frac{π}{2})} \cos (x)

$\frac{0 \cot (x) + 1}{\cot (x) - \cot (\frac{π}{2})} \cos (x)$

Reescribe

\cot (x)

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

\frac{0 \frac{\cos (x)}{\sin (x)} + 1}{\cot (x) - \cot (\frac{π}{2})} \cos (x)

$\frac{0 \frac{\cos (x)}{\sin (x)} + 1}{\cot (x) - \cot (\frac{π}{2})} \cos (x)$

Multiplica

0

$0$ por

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

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

\frac{0 + 1}{\cot (x) - \cot (\frac{π}{2})} \cos (x)

$\frac{0 + 1}{\cot (x) - \cot (\frac{π}{2})} \cos (x)$

Suma

0

$0$ y

1

$1$ .

\frac{1}{\cot (x) - \cot (\frac{π}{2})} \cos (x)

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

\frac{1}{\cot (x) - \cot (\frac{π}{2})} \cos (x)

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

Step 3

Simplifica el denominador.

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Reescribe

\cot (x)

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

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

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

El valor exacto de

\cot (\frac{π}{2})

$\cot (\frac{π}{2})$ es

0

$0$ .

\frac{1}{\frac{\cos (x)}{\sin (x)} - 0} \cos (x)

$\frac{1}{\frac{\cos (x)}{\sin (x)} - 0} \cos (x)$

Multiplica

- 1

$- 1$ por

0

$0$ .

\frac{1}{\frac{\cos (x)}{\sin (x)} + 0} \cos (x)

$\frac{1}{\frac{\cos (x)}{\sin (x)} + 0} \cos (x)$

Suma

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

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

0

$0$ .

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

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

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

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

Step 4

Multiplica el numerador por la recíproca del denominador.

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

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

Step 5

Multiplica

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

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

1

$1$ .

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

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

Step 6

Cancela el factor común de

\cos (x)

$\cos (x)$ .

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Cancela el factor común.

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

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

Reescribe la expresión.

\sin (x)

$\sin (x)$

\sin (x)

$\sin (x)$