es

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tan(x/2-pi/2)=sqrt(2)

Solución

tan (\frac{x}{2} - \frac{π}{2}) = 2

Solución

x = 2 \cdot 0.95531 \dots + 2 πn + π

+1

Grados

x = 289.47122 \dots^{\circ} + 36 0^{\circ} n

Pasos de solución

tan (\frac{x}{2} - \frac{π}{2}) = 2

Aplicar propiedades trigonométricas inversas

tan (\frac{x}{2} - \frac{π}{2}) = 2

Soluciones generales para

tan (\frac{x}{2} - \frac{π}{2}) = 2

tan (x) = a \Rightarrow x = arctan (a) + πn

\frac{x}{2} - \frac{π}{2} = arctan (2) + πn

\frac{x}{2} - \frac{π}{2} = arctan (2) + πn

Resolver

\frac{x}{2} - \frac{π}{2} = arctan (2) + πn : x = 2 arctan (2) + 2 πn + π

\frac{x}{2} - \frac{π}{2} = arctan (2) + πn

Mover

\frac{π}{2}

al lado derecho

\frac{x}{2} - \frac{π}{2} = arctan (2) + πn

Sumar

\frac{π}{2}

a ambos lados

\frac{x}{2} - \frac{π}{2} + \frac{π}{2} = arctan (2) + πn + \frac{π}{2}

Simplificar

\frac{x}{2} = arctan (2) + πn + \frac{π}{2}

\frac{x}{2} = arctan (2) + πn + \frac{π}{2}

Multiplicar ambos lados por

2

\frac{x}{2} = arctan (2) + πn + \frac{π}{2}

Multiplicar ambos lados por

2

\frac{2 x}{2} = 2 arctan (2) + 2 πn + 2 \cdot \frac{π}{2}

Simplificar

\frac{2 x}{2} = 2 arctan (2) + 2 πn + 2 \cdot \frac{π}{2}

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

2 arctan (2) + 2 πn + 2 \cdot \frac{π}{2} : 2 arctan (2) + 2 πn + π

2 arctan (2) + 2 πn + 2 \cdot \frac{π}{2}

2 \cdot \frac{π}{2} = π

2 \cdot \frac{π}{2}

Multiplicar fracciones:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{π 2}{2}

Eliminar los terminos comunes:

2

= π

= 2 arctan (2) + 2 πn + π

x = 2 arctan (2) + 2 πn + π

x = 2 arctan (2) + 2 πn + π

x = 2 arctan (2) + 2 πn + π

x = 2 arctan (2) + 2 πn + π

Mostrar soluciones en forma decimal

x = 2 \cdot 0.95531 \dots + 2 πn + π

Ejemplos populares

8sec(x)+8tan(x)=8

8 sec (x) + 8 tan (x) = 8

25cot^2(θ)-16=0

25 cot^{2} (θ) - 16 = 0

2sin^2(x)=sin(x)+1

2 sin^{2} (x) = sin (x) + 1

sin(3x)=-(sqrt(3))/2

sin (3 x) = - \frac{3}{2}

3sin(2x)sin(x)=3cos(x)

3 sin (2 x) sin (x) = 3 cos (x)