English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

verificar tan(135+a)=(tan(a)-1)/(tan(a)+1)

Solución

verificar

tan (13 5^{\circ} + a) = \frac{tan ( a ) - 1}{tan ( a ) + 1}

Solución

Verdadero

Pasos de solución

tan (13 5^{\circ} + a) = \frac{tan ( a ) - 1}{tan ( a ) + 1}

Manipular el lado derecho

tan (13 5^{\circ} + a)

Re-escribir usando identidades trigonométricas

tan (13 5^{\circ} + a)

Utilizar la identidad trigonométrica básica:

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

= \frac{sin ( 13 5 ^{\circ} + a )}{cos ( 13 5 ^{\circ} + a )}

Utilizar la identidad de suma de ángulos:

sin (s + t) = sin (s) cos (t) + cos (s) sin (t)

= \frac{sin ( 13 5 ^{\circ} ) cos ( a ) + cos ( 13 5 ^{\circ} ) sin ( a )}{cos ( 13 5 ^{\circ} + a )}

Utilizar la identidad de suma de ángulos:

cos (s + t) = cos (s) cos (t) - sin (s) sin (t)

= \frac{sin ( 13 5 ^{\circ} ) cos ( a ) + cos ( 13 5 ^{\circ} ) sin ( a )}{cos ( 13 5 ^{\circ} ) cos ( a ) - sin ( 13 5 ^{\circ} ) sin ( a )}

Simplificar

\frac{sin ( 13 5 ^{\circ} ) cos ( a ) + cos ( 13 5 ^{\circ} ) sin ( a )}{cos ( 13 5 ^{\circ} ) cos ( a ) - sin ( 13 5 ^{\circ} ) sin ( a )} : - \frac{cos ( a ) - sin ( a )}{cos ( a ) + sin ( a )}

\frac{sin ( 13 5 ^{\circ} ) cos ( a ) + cos ( 13 5 ^{\circ} ) sin ( a )}{cos ( 13 5 ^{\circ} ) cos ( a ) - sin ( 13 5 ^{\circ} ) sin ( a )}

sin (13 5^{\circ}) cos (a) + cos (13 5^{\circ}) sin (a) = \frac{2}{2} cos (a) - \frac{2}{2} sin (a)

sin (13 5^{\circ}) cos (a) + cos (13 5^{\circ}) sin (a)

Simplificar

sin (13 5^{\circ}) : \frac{2}{2}

sin (13 5^{\circ})

Utilizar la siguiente identidad trivial:

sin (13 5^{\circ}) = \frac{2}{2}

tabla de valores periódicos con

36 0^{\circ} n

intervalos:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{2}{2}

= \frac{2}{2} cos (a) + cos (13 5^{\circ}) sin (a)

Simplificar

cos (13 5^{\circ}) : - \frac{2}{2}

cos (13 5^{\circ})

Utilizar la siguiente identidad trivial:

cos (13 5^{\circ}) = - \frac{2}{2}

cos (x)

tabla de valores periódicos con

36 0^{\circ} n

intervalos:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= - \frac{2}{2}

= \frac{2}{2} cos (a) - \frac{2}{2} sin (a)

= \frac{\frac{2}{2} cos ( a ) - \frac{2}{2} sin ( a )}{cos ( 13 5 ^{\circ} ) cos ( a ) - sin ( 13 5 ^{\circ} ) sin ( a )}

cos (13 5^{\circ}) cos (a) - sin (13 5^{\circ}) sin (a) = - \frac{2}{2} cos (a) - \frac{2}{2} sin (a)

cos (13 5^{\circ}) cos (a) - sin (13 5^{\circ}) sin (a)

Simplificar

cos (13 5^{\circ}) : - \frac{2}{2}

cos (13 5^{\circ})

Utilizar la siguiente identidad trivial:

cos (13 5^{\circ}) = - \frac{2}{2}

cos (x)

tabla de valores periódicos con

36 0^{\circ} n

intervalos:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= - \frac{2}{2}

= - \frac{2}{2} cos (a) - sin (13 5^{\circ}) sin (a)

Simplificar

sin (13 5^{\circ}) : \frac{2}{2}

sin (13 5^{\circ})

Utilizar la siguiente identidad trivial:

sin (13 5^{\circ}) = \frac{2}{2}

tabla de valores periódicos con

36 0^{\circ} n

intervalos:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{2}{2}

= - \frac{2}{2} cos (a) - \frac{2}{2} sin (a)

= \frac{\frac{2}{2} cos ( a ) - \frac{2}{2} sin ( a )}{- \frac{2}{2} cos ( a ) - \frac{2}{2} sin ( a )}

Multiplicar

\frac{2}{2} cos (a) : \frac{2 cos ( a )}{2}

\frac{2}{2} cos (a)

Multiplicar fracciones:

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

= \frac{2 cos ( a )}{2}

= \frac{\frac{2}{2} cos ( a ) - \frac{2}{2} sin ( a )}{- \frac{2 c o s ( a )}{2} - \frac{2}{2} sin ( a )}

Multiplicar

\frac{2}{2} sin (a) : \frac{2 sin ( a )}{2}

\frac{2}{2} sin (a)

Multiplicar fracciones:

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

= \frac{2 sin ( a )}{2}

= \frac{\frac{2}{2} cos ( a ) - \frac{2}{2} sin ( a )}{- \frac{2 c o s ( a )}{2} - \frac{2 s i n ( a )}{2}}

Multiplicar

\frac{2}{2} cos (a) : \frac{2 cos ( a )}{2}

\frac{2}{2} cos (a)

Multiplicar fracciones:

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

= \frac{2 cos ( a )}{2}

= \frac{\frac{2 c o s ( a )}{2} - \frac{2}{2} sin ( a )}{- \frac{2 c o s ( a )}{2} - \frac{2 s i n ( a )}{2}}

Multiplicar

\frac{2}{2} sin (a) : \frac{2 sin ( a )}{2}

\frac{2}{2} sin (a)

Multiplicar fracciones:

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

= \frac{2 sin ( a )}{2}

= \frac{\frac{2 c o s ( a )}{2} - \frac{2 s i n ( a )}{2}}{- \frac{2 c o s ( a )}{2} - \frac{2 s i n ( a )}{2}}

Combinar las fracciones usando el mínimo común denominador:

\frac{- 2 cos ( a ) - 2 sin ( a )}{2}

Aplicar la regla

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

= \frac{- 2 cos ( a ) - 2 sin ( a )}{2}

= \frac{\frac{2 c o s ( a )}{2} - \frac{2 s i n ( a )}{2}}{\frac{- 2 c o s ( a ) - 2 s i n ( a )}{2}}

Combinar las fracciones usando el mínimo común denominador:

\frac{2 cos ( a ) - 2 sin ( a )}{2}

Aplicar la regla

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

= \frac{2 cos ( a ) - 2 sin ( a )}{2}

= \frac{\frac{2 c o s ( a ) - 2 s i n ( a )}{2}}{\frac{- 2 c o s ( a ) - 2 s i n ( a )}{2}}

Dividir fracciones:

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

= \frac{( 2 cos ( a ) - 2 sin ( a ) ) \cdot 2}{2 ( - 2 cos ( a ) - 2 sin ( a ) )}

Eliminar los terminos comunes:

2

= \frac{2 cos ( a ) - 2 sin ( a )}{- 2 cos ( a ) - 2 sin ( a )}

Factorizar el termino común

2

= \frac{2 ( cos ( a ) - sin ( a ) )}{- 2 cos ( a ) - 2 sin ( a )}

Factorizar el termino común

2

= - \frac{2 ( cos ( a ) - sin ( a ) )}{2 ( cos ( a ) + sin ( a ) )}

Eliminar los terminos comunes:

2

= - \frac{cos ( a ) - sin ( a )}{cos ( a ) + sin ( a )}

= - \frac{cos ( a ) - sin ( a )}{cos ( a ) + sin ( a )}

= - \frac{cos ( a ) - sin ( a )}{cos ( a ) + sin ( a )}

= \frac{- ( cos ( a ) - sin ( a ) )}{cos ( a ) + sin ( a )}

Simplificar

= \frac{- cos ( a ) + sin ( a )}{cos ( a ) + sin ( a )}

Manipular el lado izquierdo

\frac{tan ( a ) - 1}{tan ( a ) + 1}

Expresar con seno, coseno

\frac{- 1 + tan ( a )}{1 + tan ( a )}

Utilizar la identidad trigonométrica básica:

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

= \frac{- 1 + \frac{s i n ( a )}{c o s ( a )}}{1 + \frac{s i n ( a )}{c o s ( a )}}

Simplificar

\frac{- 1 + \frac{s i n ( a )}{c o s ( a )}}{1 + \frac{s i n ( a )}{c o s ( a )}} : \frac{- cos ( a ) + sin ( a )}{cos ( a ) + sin ( a )}

\frac{- 1 + \frac{s i n ( a )}{c o s ( a )}}{1 + \frac{s i n ( a )}{c o s ( a )}}

Simplificar

1 + \frac{sin ( a )}{cos ( a )}

en una fracción:

\frac{cos ( a ) + sin ( a )}{cos ( a )}

1 + \frac{sin ( a )}{cos ( a )}

Convertir a fracción:

1 = \frac{1 cos ( a )}{cos ( a )}

= \frac{1 \cdot cos ( a )}{cos ( a )} + \frac{sin ( a )}{cos ( a )}

Ya que los denominadores son iguales, combinar las fracciones:

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

= \frac{1 \cdot cos ( a ) + sin ( a )}{cos ( a )}

Multiplicar:

1 \cdot cos (a) = cos (a)

= \frac{cos ( a ) + sin ( a )}{cos ( a )}

= \frac{- 1 + \frac{s i n ( a )}{c o s ( a )}}{\frac{c o s ( a ) + s i n ( a )}{c o s ( a )}}

Simplificar

- 1 + \frac{sin ( a )}{cos ( a )}

en una fracción:

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

- 1 + \frac{sin ( a )}{cos ( a )}

Convertir a fracción:

1 = \frac{1 cos ( a )}{cos ( a )}

= - \frac{1 \cdot cos ( a )}{cos ( a )} + \frac{sin ( a )}{cos ( a )}

Ya que los denominadores son iguales, combinar las fracciones:

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

= \frac{- 1 \cdot cos ( a ) + sin ( a )}{cos ( a )}

Multiplicar:

1 \cdot cos (a) = cos (a)

= \frac{- cos ( a ) + sin ( a )}{cos ( a )}

= \frac{\frac{- c o s ( a ) + s i n ( a )}{c o s ( a )}}{\frac{c o s ( a ) + s i n ( a )}{c o s ( a )}}

Dividir fracciones:

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

= \frac{( - cos ( a ) + sin ( a ) ) cos ( a )}{cos ( a ) ( cos ( a ) + sin ( a ) )}

Eliminar los terminos comunes:

cos (a)

= \frac{- cos ( a ) + sin ( a )}{cos ( a ) + sin ( a )}

= \frac{- cos ( a ) + sin ( a )}{cos ( a ) + sin ( a )}

= \frac{- cos ( a ) + sin ( a )}{cos ( a ) + sin ( a )}

Se demostró que ambos lados pueden tomar la misma forma

\Rightarrow Verdadero

Ejemplos populares

verificar tan(x/2)=(tan(x))/((sec(x)+1))verificar

tan (\frac{x}{2}) = \frac{tan ( x )}{( sec ( x ) + 1 )}

verificar-cos^2(x)tan^2(x)=-sin^2(x)verificar

- cos^{2} (x) tan^{2} (x) = - sin^{2} (x)

verificar sin(x)-1/(sin(x))=-cos(x)cot(x)verificar

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

verificar 2cos^2(x)-cos(x)-1=0 verificar

2 cos^{2} (x) - cos (x) - 1 = 0

verificar cos(θ)=cot(θ)sin^2(θ)csc(θ)verificar

cos (θ) = cot (θ) sin^{2} (θ) csc (θ)