Trigonometría Ejemplos

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

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

Step 1

Simplifica el numerador.

Toca para ver más pasos...

Aplica la razón del ángulo doble sinusoidal.

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

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

Usa la razón del ángulo doble para transformar

cos (2 x)

$\cos (2 x)$ a

2 {cos}^{2} (x) - 1

$2 \cos^{2} (x) - 1$ .

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

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

Resta

1

$1$ de

1

$1$ .

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

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

Suma

0

$0$ y

2 sin (x) cos (x)

$2 \sin (x) \cos (x)$ .

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

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

Factoriza

2 cos (x)

$2 \cos (x)$ de

2 sin (x) cos (x) + 2 {cos}^{2} (x)

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

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Factoriza

2 cos (x)

$2 \cos (x)$ de

2 sin (x) cos (x)

$2 \sin (x) \cos (x)$ .

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

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

Factoriza

2 cos (x)

$2 \cos (x)$ de

2 {cos}^{2} (x)

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

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

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

Factoriza

2 cos (x)

$2 \cos (x)$ de

2 cos (x) (sin (x)) + 2 cos (x) (cos (x))

$2 \cos (x) (\sin (x)) + 2 \cos (x) (\cos (x))$ .

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

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

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

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

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

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

Step 2

Simplifica el denominador.

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Aplica la razón del ángulo doble sinusoidal.

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

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

Usa la razón del ángulo doble para transformar

cos (2 x)

$\cos (2 x)$ a

2 {cos}^{2} (x) - 1

$2 \cos^{2} (x) - 1$ .

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

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

Aplica la propiedad distributiva.

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

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

Multiplica

2

$2$ por

- 1

$- 1$ .

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

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

Multiplica

- 1

$- 1$ por

- 1

$- 1$ .

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

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

Suma

1

$1$ y

1

$1$ .

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

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

Factoriza

2

$2$ de

2 + 2 sin (x) cos (x) - 2 {cos}^{2} (x)

$2 + 2 \sin (x) \cos (x) - 2 \cos^{2} (x)$ .

Toca para ver más pasos...

Factoriza

2

$2$ de

2

$2$ .

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

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

Factoriza

2

$2$ de

2 sin (x) cos (x)

$2 \sin (x) \cos (x)$ .

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

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

Factoriza

2

$2$ de

- 2 {cos}^{2} (x)

$- 2 \cos^{2} (x)$ .

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

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

Factoriza

2

$2$ de

2 (1) + 2 (sin (x) cos (x))

$2 (1) + 2 (\sin (x) \cos (x))$ .

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

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

Factoriza

2

$2$ de

2 (1 + sin (x) cos (x)) + 2 (- {cos}^{2} (x))

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

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

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

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

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

Mueve

- {cos}^{2} (x)

$- \cos^{2} (x)$ .

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

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

Aplica la identidad pitagórica.

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

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

Factoriza

sin (x)

$\sin (x)$ de

{sin}^{2} (x) + sin (x) cos (x)

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

Toca para ver más pasos...

Factoriza

sin (x)

$\sin (x)$ de

{sin}^{2} (x)

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

\frac{2 cos (x) (sin (x) + cos (x))}{2 (sin (x) sin (x) + sin (x) cos (x))}

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

Factoriza

sin (x)

$\sin (x)$ de

sin (x) cos (x)

$\sin (x) \cos (x)$ .

\frac{2 cos (x) (sin (x) + cos (x))}{2 (sin (x) sin (x) + sin (x) (cos (x)))}

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

Factoriza

sin (x)

$\sin (x)$ de

sin (x) sin (x) + sin (x) (cos (x))

$\sin (x) \sin (x) + \sin (x) (\cos (x))$ .

\frac{2 cos (x) (sin (x) + cos (x))}{2 (sin (x) (sin (x) + cos (x)))}

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

\frac{2 cos (x) (sin (x) + cos (x))}{2 sin (x) (sin (x) + cos (x))}

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

\frac{2 cos (x) (sin (x) + cos (x))}{2 sin (x) (sin (x) + cos (x))}

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

Step 3

Reduce la expresión mediante la cancelación de los factores comunes.

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Cancela el factor común de

2

$2$ .

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Cancela el factor común.

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

Reescribe la expresión.

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

Cancela el factor común de

$\sin (x) + \cos (x)$ .

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Cancela el factor común.

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

Reescribe la expresión.

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

Step 4

Convierte de

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

$\cot (x)$ .

$\cot (x)$