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solvefor x,z=tan(x^3y^2)

Solución

resolver para

x, z = tan (x^{3} y^{2})

x = 3 \frac{arctan ( z ) + πn}{y ^{2}}

Pasos de solución

z = tan (x^{3} y^{2})

Intercambiar lados

tan (x^{3} y^{2}) = z

Aplicar propiedades trigonométricas inversas

tan (x^{3} y^{2}) = z

Soluciones generales para

tan (x^{3} y^{2}) = z

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

x^{3} y^{2} = arctan (z) + πn

x^{3} y^{2} = arctan (z) + πn

Resolver

x^{3} y^{2} = arctan (z) + πn : x = 3 \frac{arctan ( z ) + πn}{y ^{2}}; y \neq = 0

x^{3} y^{2} = arctan (z) + πn

Dividir ambos lados entre

y^{2}; y \neq = 0

x^{3} y^{2} = arctan (z) + πn

Dividir ambos lados entre

y^{2}; y \neq = 0

\frac{x ^{3} y ^{2}}{y ^{2}} = \frac{arctan ( z )}{y ^{2}} + \frac{πn}{y ^{2}}; y \neq = 0

Simplificar

x^{3} = \frac{arctan ( z )}{y ^{2}} + \frac{πn}{y ^{2}}; y \neq = 0

x^{3} = \frac{arctan ( z )}{y ^{2}} + \frac{πn}{y ^{2}}; y \neq = 0

Para

x^{n} = f (a)

, n es impar, la solución es

x = n f (a)

x = 3 \frac{arctan ( z )}{y ^{2}} + \frac{πn}{y ^{2}}; y \neq = 0

Simplificar

3 \frac{arctan ( z )}{y ^{2}} + \frac{πn}{y ^{2}} : 3 \frac{arctan ( z ) + πn}{y ^{2}}

3 \frac{arctan ( z )}{y ^{2}} + \frac{πn}{y ^{2}}

Combinar las fracciones usando el mínimo común denominador:

\frac{arctan ( z ) + πn}{y ^{2}}

Aplicar la regla

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

= \frac{arctan ( z ) + πn}{y ^{2}}

= 3 \frac{arctan ( z ) + πn}{y ^{2}}

x = 3 \frac{arctan ( z ) + πn}{y ^{2}}; y \neq = 0

x = 3 \frac{arctan ( z ) + πn}{y ^{2}}

sin^{4} (x) = - 2 sin^{2} (x)

3 tan (4 x) = 2

- cos (2 x) = 0

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

2 cot^{2} (x) - 3 csc (x) = 0