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(1-tan^2(A))/(1+tan^2(A))=1

Solución

\frac{1 - tan ^{2} ( A )}{1 + tan ^{2} ( A )} = 1

Solución

A = πn

+1

Grados

A = 0^{\circ} + 18 0^{\circ} n

Pasos de solución

\frac{1 - tan ^{2} ( A )}{1 + tan ^{2} ( A )} = 1

Usando el método de sustitución

\frac{1 - tan ^{2} ( A )}{1 + tan ^{2} ( A )} = 1

Sea:

tan (A) = u

\frac{1 - u ^{2}}{1 + u ^{2}} = 1

\frac{1 - u ^{2}}{1 + u ^{2}} = 1 : u = 0

\frac{1 - u ^{2}}{1 + u ^{2}} = 1

Multiplicar ambos lados por

1 + u^{2}

\frac{1 - u ^{2}}{1 + u ^{2}} = 1

Multiplicar ambos lados por

1 + u^{2}

\frac{1 - u ^{2}}{1 + u ^{2}} (1 + u^{2}) = 1 \cdot (1 + u^{2})

Simplificar

\frac{1 - u ^{2}}{1 + u ^{2}} (1 + u^{2}) = 1 \cdot (1 + u^{2})

Simplificar

\frac{1 - u ^{2}}{1 + u ^{2}} (1 + u^{2}) : 1 - u^{2}

\frac{1 - u ^{2}}{1 + u ^{2}} (1 + u^{2})

Multiplicar fracciones:

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

= \frac{( 1 - u ^{2} ) ( 1 + u ^{2} )}{1 + u ^{2}}

Eliminar los terminos comunes:

1 + u^{2}

= 1 - u^{2}

Simplificar

1 \cdot (1 + u^{2}) : 1 + u^{2}

1 \cdot (1 + u^{2})

Multiplicar:

1 \cdot (1 + u^{2}) = (1 + u^{2})

= (1 + u^{2})

Quitar los parentesis:

(a) = a

= 1 + u^{2}

1 - u^{2} = 1 + u^{2}

1 - u^{2} = 1 + u^{2}

1 - u^{2} = 1 + u^{2}

Resolver

1 - u^{2} = 1 + u^{2} : u = 0

1 - u^{2} = 1 + u^{2}

Mover

1

al lado derecho

1 - u^{2} = 1 + u^{2}

Restar

1

de ambos lados

1 - u^{2} - 1 = 1 + u^{2} - 1

Simplificar

- u^{2} = u^{2}

- u^{2} = u^{2}

Mover

u^{2}

al lado izquierdo

- u^{2} = u^{2}

Restar

u^{2}

de ambos lados

- u^{2} - u^{2} = u^{2} - u^{2}

Simplificar

- 2 u^{2} = 0

- 2 u^{2} = 0

Dividir ambos lados entre

- 2

- 2 u^{2} = 0

Dividir ambos lados entre

- 2

- 2 u^{2} = 0

Dividir ambos lados entre

- 2

\frac{- 2 u ^{2}}{- 2} = \frac{0}{- 2}

Simplificar

u^{2} = 0

u^{2} = 0

Aplicar la regla

x^{n} = 0 \Rightarrow x = 0

u = 0

u = 0

Sustituir en la ecuación

u = tan (A)

tan (A) = 0

tan (A) = 0

tan (A) = 0 : A = πn

tan (A) = 0

Soluciones generales para

tan (A) = 0

tan (x)

tabla de valores periódicos con

πn

intervalos:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

A = 0 + πn

A = 0 + πn

Resolver

A = 0 + πn : A = πn

A = 0 + πn

0 + πn = πn

A = πn

A = πn

Combinar toda las soluciones

A = πn

Ejemplos populares

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2cos^2(θ)+sin(θ)=2

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tanh^2(x)+5sech(x)-5=0

tanh^{2} (x) + 5 sech (x) - 5 = 0

solvefor a,P=cot^2(a)resolver para

a, P = cot^{2} (a)