Trigonometría Ejemplos

\tan (A) = \tan (A) \cdot \csc^{2} (A) + \cot (- A)

$\tan (A) = \tan (A) \cdot \csc^{2} (A) + \cot (- A)$

Step 1

Comienza por el lado derecho.

\tan (A) \cdot \csc^{2} (A) + \cot (- A)

$\tan (A) \cdot \csc^{2} (A) + \cot (- A)$

Step 2

Como

\cot (- A)

$\cot (- A)$ es una función impar, reescribe

\cot (- A)

$\cot (- A)$ como

- \cot (A)

$- \cot (A)$ .

\tan (A) \cdot \csc^{2} (A) - \cot (A)

$\tan (A) \cdot \csc^{2} (A) - \cot (A)$

Step 3

Aplica la identidad pitagórica al revés.

\tan (A) \cdot (1 + \cot^{2} (A)) - \cot (A)

$\tan (A) \cdot (1 + \cot^{2} (A)) - \cot (A)$

Step 4

Convierte a senos y cosenos.

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Escribe

\tan (A)

$\tan (A)$ en senos y cosenos mediante la identidad del cociente.

\frac{\sin (A)}{\cos (A)} \cdot (1 + \cot^{2} (A)) - \cot (A)

$\frac{\sin (A)}{\cos (A)} \cdot (1 + \cot^{2} (A)) - \cot (A)$

Escribe

\cot (A)

$\cot (A)$ en senos y cosenos mediante la identidad del cociente.

\frac{\sin (A)}{\cos (A)} \cdot (1 + {(\frac{\cos (A)}{\sin (A)})}^{2}) - \cot (A)

$\frac{\sin (A)}{\cos (A)} \cdot (1 + {(\frac{\cos (A)}{\sin (A)})}^{2}) - \cot (A)$

Escribe

\cot (A)

$\cot (A)$ en senos y cosenos mediante la identidad del cociente.

\frac{\sin (A)}{\cos (A)} \cdot (1 + {(\frac{\cos (A)}{\sin (A)})}^{2}) - \frac{\cos (A)}{\sin (A)}

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

Aplica la regla del producto a

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

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

\frac{\sin (A)}{\cos (A)} \cdot (1 + \frac{\cos^{2} (A)}{\sin^{2} (A)}) - \frac{\cos (A)}{\sin (A)}

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

\frac{\sin (A)}{\cos (A)} \cdot (1 + \frac{\cos^{2} (A)}{\sin^{2} (A)}) - \frac{\cos (A)}{\sin (A)}

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

Step 5

Simplifica.

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Simplifica cada término.

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Aplica la propiedad distributiva.

\frac{\sin (A)}{\cos (A)} \cdot 1 + \frac{\sin (A)}{\cos (A)} \cdot \frac{{\cos (A)}^{2}}{{\sin (A)}^{2}} - \frac{\cos (A)}{\sin (A)}

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

Multiplica

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

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

1

$1$ .

\frac{\sin (A)}{\cos (A)} + \frac{\sin (A)}{\cos (A)} \cdot \frac{{\cos (A)}^{2}}{{\sin (A)}^{2}} - \frac{\cos (A)}{\sin (A)}

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

Combinar.

\frac{\sin (A)}{\cos (A)} + \frac{\sin (A) {\cos (A)}^{2}}{\cos (A) {\sin (A)}^{2}} - \frac{\cos (A)}{\sin (A)}

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

Simplifica cada término.

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Cancela el factor común de

\sin (A)

$\sin (A)$ y

{\sin (A)}^{2}

${\sin (A)}^{2}$ .

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Factoriza

\sin (A)

$\sin (A)$ de

\sin (A) {\cos (A)}^{2}

$\sin (A) {\cos (A)}^{2}$ .

\frac{\sin (A)}{\cos (A)} + \frac{\sin (A) ({\cos (A)}^{2})}{\cos (A) {\sin (A)}^{2}} - \frac{\cos (A)}{\sin (A)}

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

Cancela los factores comunes.

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Factoriza

\sin (A)

$\sin (A)$ de

\cos (A) {\sin (A)}^{2}

$\cos (A) {\sin (A)}^{2}$ .

\frac{\sin (A)}{\cos (A)} + \frac{\sin (A) ({\cos (A)}^{2})}{\sin (A) (\cos (A) \sin (A))} - \frac{\cos (A)}{\sin (A)}

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

Cancela el factor común.

\frac{\sin (A)}{\cos (A)} + \frac{\sin (A) {\cos (A)}^{2}}{\sin (A) (\cos (A) \sin (A))} - \frac{\cos (A)}{\sin (A)}

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

Reescribe la expresión.

\frac{\sin (A)}{\cos (A)} + \frac{{\cos (A)}^{2}}{\cos (A) \sin (A)} - \frac{\cos (A)}{\sin (A)}

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

\frac{\sin (A)}{\cos (A)} + \frac{{\cos (A)}^{2}}{\cos (A) \sin (A)} - \frac{\cos (A)}{\sin (A)}

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

\frac{\sin (A)}{\cos (A)} + \frac{{\cos (A)}^{2}}{\cos (A) \sin (A)} - \frac{\cos (A)}{\sin (A)}

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

Cancela el factor común de

{\cos (A)}^{2}

${\cos (A)}^{2}$ y

\cos (A)

$\cos (A)$ .

Toca para ver más pasos...

Factoriza

\cos (A)

$\cos (A)$ de

{\cos (A)}^{2}

${\cos (A)}^{2}$ .

\frac{\sin (A)}{\cos (A)} + \frac{\cos (A) \cos (A)}{\cos (A) \sin (A)} - \frac{\cos (A)}{\sin (A)}

$\frac{\sin (A)}{\cos (A)} + \frac{\cos (A) \cos (A)}{\cos (A) \sin (A)} - \frac{\cos (A)}{\sin (A)}$

Cancela los factores comunes.

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Factoriza

\cos (A)

$\cos (A)$ de

\cos (A) \sin (A)

$\cos (A) \sin (A)$ .

\frac{\sin (A)}{\cos (A)} + \frac{\cos (A) \cos (A)}{\cos (A) (\sin (A))} - \frac{\cos (A)}{\sin (A)}

$\frac{\sin (A)}{\cos (A)} + \frac{\cos (A) \cos (A)}{\cos (A) (\sin (A))} - \frac{\cos (A)}{\sin (A)}$

Cancela el factor común.

\frac{\sin (A)}{\cos (A)} + \frac{\cos (A) \cos (A)}{\cos (A) \sin (A)} - \frac{\cos (A)}{\sin (A)}

$\frac{\sin (A)}{\cos (A)} + \frac{\cos (A) \cos (A)}{\cos (A) \sin (A)} - \frac{\cos (A)}{\sin (A)}$

Reescribe la expresión.

\frac{\sin (A)}{\cos (A)} + \frac{\cos (A)}{\sin (A)} - \frac{\cos (A)}{\sin (A)}