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solvefor x,cot(-x)cos(-x)+sin(-x)=-1/f

Solución

resolver para

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

Solución

x = arcsin (f) + 2 πn, x = π + arcsin (- f) + 2 πn

Pasos de solución

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

Re-escribir usando identidades trigonométricas

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

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

Simplificar

- sin (x) + cos (x) (- cot (x)) : - sin (x) - cos (x) cot (x)

- sin (x) + cos (x) (- cot (x))

Quitar los parentesis:

(- a) = - a

= - sin (x) - cos (x) cot (x)

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

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

Restar

- \frac{1}{f}

de ambos lados

- sin (x) - cos (x) cot (x) + \frac{1}{f} = 0

Simplificar

- sin (x) - cos (x) cot (x) + \frac{1}{f} : \frac{- f sin ( x ) - f cos ( x ) cot ( x ) + 1}{f}

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

Convertir a fracción:

sin (x) = \frac{sin ( x ) f}{f}, cos (x) cot (x) = \frac{cos ( x ) cot ( x ) f}{f}

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

Ya que los denominadores son iguales, combinar las fracciones:

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

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

\frac{- f sin ( x ) - f cos ( x ) cot ( x ) + 1}{f} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

- f sin (x) - f cos (x) cot (x) + 1 = 0

Re-escribir usando identidades trigonométricas

1 - sin (x) f - cos (x) cot (x) f

Utilizar la identidad trigonométrica básica:

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

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

cos (x) \frac{cos ( x )}{sin ( x )} f = \frac{f cos ^{2} ( x )}{sin ( x )}

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

Multiplicar fracciones:

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

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

cos (x) cos (x) f = f cos^{2} (x)

cos (x) cos (x) f

Aplicar las leyes de los exponentes:

a^{b} \cdot a^{c} = a^{b + c}

cos (x) cos (x) = cos^{1 + 1} (x)

= cos^{1 + 1} (x) f

Sumar:

1 + 1 = 2

= cos^{2} (x) f

= \frac{f cos ^{2} ( x )}{sin ( x )}

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

Utilizar la identidad pitagórica:

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

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

= 1 - \frac{( 1 - sin ^{2} ( x ) ) f}{sin ( x )} - sin (x) f

Combinar las fracciones usando el mínimo común denominador:

- \frac{f}{sin ( x )}

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

Convertir a fracción:

f sin (x) = \frac{sin ( x ) f sin ( x )}{sin ( x )}

= - \frac{( 1 - sin ^{2} ( x ) ) f}{sin ( x )} - \frac{sin ( x ) f sin ( x )}{sin ( x )}

Ya que los denominadores son iguales, combinar las fracciones:

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

= \frac{- ( 1 - sin ^{2} ( x ) ) f - sin ( x ) f sin ( x )}{sin ( x )}

- (1 - sin^{2} (x)) f - sin (x) f sin (x) = - f (1 - sin^{2} (x)) - f sin^{2} (x)

- (1 - sin^{2} (x)) f - sin (x) f sin (x)

sin (x) f sin (x) = f sin^{2} (x)

sin (x) f sin (x)

Aplicar las leyes de los exponentes:

a^{b} \cdot a^{c} = a^{b + c}

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

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

Sumar:

1 + 1 = 2

= f sin^{2} (x)

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

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

Expandir

- (1 - sin^{2} (x)) f - f sin^{2} (x) : - f

- (1 - sin^{2} (x)) f - f sin^{2} (x)

= - f (1 - sin^{2} (x)) - f sin^{2} (x)

Expandir

- f (1 - sin^{2} (x)) : - f + f sin^{2} (x)

- f (1 - sin^{2} (x))

Poner los parentesis utilizando:

a (b - c) = ab - a c

a = - f, b = 1, c = sin^{2} (x)

= - f \cdot 1 - (- f) sin^{2} (x)

Aplicar las reglas de los signos

- (- a) = a

= - 1 \cdot f + f sin^{2} (x)

Multiplicar:

1 \cdot f = f

= - f + f sin^{2} (x)

= - f + f sin^{2} (x) - f sin^{2} (x)

Sumar elementos similares:

f sin^{2} (x) - f sin^{2} (x) = 0

= - f

= \frac{- f}{sin ( x )}

Aplicar las propiedades de las fracciones:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{f}{sin ( x )}

1 - \frac{f}{sin ( x )} = 0

1 - \frac{f}{sin ( x )} = 0

Multiplicar ambos lados por

sin (x)

1 - \frac{f}{sin ( x )} = 0

Multiplicar ambos lados por

sin (x)

1 \cdot sin (x) - \frac{f}{sin ( x )} sin (x) = 0 \cdot sin (x)

Simplificar

1 \cdot sin (x) - \frac{f}{sin ( x )} sin (x) = 0 \cdot sin (x)

Simplificar

1 \cdot sin (x) : sin (x)

1 \cdot sin (x)

Multiplicar:

1 \cdot sin (x) = sin (x)

= sin (x)

Simplificar

- \frac{f}{sin ( x )} sin (x) : - f

- \frac{f}{sin ( x )} sin (x)

Multiplicar fracciones:

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

= - \frac{f sin ( x )}{sin ( x )}

Eliminar los terminos comunes:

sin (x)

= - f

Simplificar

0 \cdot sin (x) : 0

0 \cdot sin (x)

Aplicar la regla

0 \cdot a = 0

= 0

sin (x) - f = 0

sin (x) - f = 0

sin (x) - f = 0

Mover

f

al lado derecho

sin (x) - f = 0

Sumar

f

a ambos lados

sin (x) - f + f = 0 + f

Simplificar

sin (x) = f

sin (x) = f

Aplicar propiedades trigonométricas inversas

sin (x) = f

Soluciones generales para

sin (x) = f

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π + arcsin (a) + 2 πn

x = arcsin (f) + 2 πn, x = π + arcsin (- f) + 2 πn

x = arcsin (f) + 2 πn, x = π + arcsin (- f) + 2 πn

Ejemplos populares

cos(x)=-2/3

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

10cos^2(x)+5cos(x)-5=0

10 cos^{2} (x) + 5 cos (x) - 5 = 0

2sin(x)=-sqrt(3)

2 sin (x) = - 3

sqrt(3)sec(θ)-2=0

3 sec (θ) - 2 = 0

4cos(x)=1

4 cos (x) = 1