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solvefor y,-ln(cos(x))+cos(x)sin(y)=C

Solución

resolver para

y, - ln (cos (x)) + cos (x) sin (y) = C

Solución

y = arcsin (\frac{C + ln ( cos ( x ) )}{cos ( x )}) + 2 πn, y = π + arcsin (- \frac{C + ln ( cos ( x ) )}{cos ( x )}) + 2 πn

Pasos de solución

- ln (cos (x)) + cos (x) sin (y) = C

Mover

ln (cos (x))

al lado derecho

- ln (cos (x)) + cos (x) sin (y) = C

Sumar

ln (cos (x))

a ambos lados

- ln (cos (x)) + cos (x) sin (y) + ln (cos (x)) = C + ln (cos (x))

Simplificar

cos (x) sin (y) = C + ln (cos (x))

cos (x) sin (y) = C + ln (cos (x))

Dividir ambos lados entre

cos (x); x \neq = \frac{π}{2} + 2 πn, x \neq = \frac{3 π}{2} + 2 πn

cos (x) sin (y) = C + ln (cos (x))

Dividir ambos lados entre

cos (x); x \neq = \frac{π}{2} + 2 πn, x \neq = \frac{3 π}{2} + 2 πn

\frac{cos ( x ) sin ( y )}{cos ( x )} = \frac{C}{cos ( x )} + \frac{ln ( cos ( x ) )}{cos ( x )}; x \neq = \frac{π}{2} + 2 πn, x \neq = \frac{3 π}{2} + 2 πn

Simplificar

\frac{cos ( x ) sin ( y )}{cos ( x )} = \frac{C}{cos ( x )} + \frac{ln ( cos ( x ) )}{cos ( x )}

Simplificar

\frac{cos ( x ) sin ( y )}{cos ( x )} : sin (y)

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

Eliminar los terminos comunes:

cos (x)

= sin (y)

Simplificar

\frac{C}{cos ( x )} + \frac{ln ( cos ( x ) )}{cos ( x )} : \frac{C + ln ( cos ( x ) )}{cos ( x )}

\frac{C}{cos ( x )} + \frac{ln ( cos ( x ) )}{cos ( x )}

Aplicar la regla

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

= \frac{C + ln ( cos ( x ) )}{cos ( x )}

sin (y) = \frac{C + ln ( cos ( x ) )}{cos ( x )}; x \neq = \frac{π}{2} + 2 πn, x \neq = \frac{3 π}{2} + 2 πn

sin (y) = \frac{C + ln ( cos ( x ) )}{cos ( x )}; x \neq = \frac{π}{2} + 2 πn, x \neq = \frac{3 π}{2} + 2 πn

sin (y) = \frac{C + ln ( cos ( x ) )}{cos ( x )}; x \neq = \frac{π}{2} + 2 πn, x \neq = \frac{3 π}{2} + 2 πn

Aplicar propiedades trigonométricas inversas

sin (y) = \frac{C + ln ( cos ( x ) )}{cos ( x )}

Soluciones generales para

sin (y) = \frac{C + ln ( cos ( x ) )}{cos ( x )}

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

y = arcsin (\frac{C + ln ( cos ( x ) )}{cos ( x )}) + 2 πn, y = π + arcsin (- \frac{C + ln ( cos ( x ) )}{cos ( x )}) + 2 πn

y = arcsin (\frac{C + ln ( cos ( x ) )}{cos ( x )}) + 2 πn, y = π + arcsin (- \frac{C + ln ( cos ( x ) )}{cos ( x )}) + 2 πn

Ejemplos populares

4tan(θ)=5-tan(θ)

4 tan (θ) = 5 - tan (θ)

2 sec (x) = 1

sin(2x)=cos(x),0<= <2pi

sin (2 x) = cos (x), 0 \leq < 2 π

solvefor x,y^1=sin(x)resolver para

x, y^{1} = sin (x)

tan (θ) = \frac{15}{6}