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العربية

(tan^2(b)+1)/((tan(x)))=csc^2(b)

Solución

\frac{tan ^{2} ( b ) + 1}{( tan ( x ) )} = csc^{2} (b)

x = arctan (\frac{tan ^{2} ( b ) + 1}{csc ^{2} ( b )}) + πn

Pasos de solución

\frac{tan ^{2} ( b ) + 1}{( tan ( x ) )} = csc^{2} (b)

Multiplicar ambos lados por

tan (x)

\frac{tan ^{2} ( b ) + 1}{tan ( x )} = csc^{2} (b)

Multiplicar ambos lados por

tan (x)

\frac{tan ^{2} ( b ) + 1}{tan ( x )} tan (x) = csc^{2} (b) tan (x)

Simplificar

tan^{2} (b) + 1 = csc^{2} (b) tan (x)

tan^{2} (b) + 1 = csc^{2} (b) tan (x)

Intercambiar lados

csc^{2} (b) tan (x) = tan^{2} (b) + 1

Dividir ambos lados entre

csc^{2} (b)

csc^{2} (b) tan (x) = tan^{2} (b) + 1

Dividir ambos lados entre

csc^{2} (b)

\frac{csc ^{2} ( b ) tan ( x )}{csc ^{2} ( b )} = \frac{tan ^{2} ( b )}{csc ^{2} ( b )} + \frac{1}{csc ^{2} ( b )}

Simplificar

\frac{csc ^{2} ( b ) tan ( x )}{csc ^{2} ( b )} = \frac{tan ^{2} ( b )}{csc ^{2} ( b )} + \frac{1}{csc ^{2} ( b )}

Simplificar

\frac{csc ^{2} ( b ) tan ( x )}{csc ^{2} ( b )} : tan (x)

\frac{csc ^{2} ( b ) tan ( x )}{csc ^{2} ( b )}

Eliminar los terminos comunes:

csc^{2} (b)

= tan (x)

Simplificar

\frac{tan ^{2} ( b )}{csc ^{2} ( b )} + \frac{1}{csc ^{2} ( b )} : \frac{tan ^{2} ( b ) + 1}{csc ^{2} ( b )}

\frac{tan ^{2} ( b )}{csc ^{2} ( b )} + \frac{1}{csc ^{2} ( b )}

Aplicar la regla

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

= \frac{tan ^{2} ( b ) + 1}{csc ^{2} ( b )}

tan (x) = \frac{tan ^{2} ( b ) + 1}{csc ^{2} ( b )}

tan (x) = \frac{tan ^{2} ( b ) + 1}{csc ^{2} ( b )}

tan (x) = \frac{tan ^{2} ( b ) + 1}{csc ^{2} ( b )}

Aplicar propiedades trigonométricas inversas

tan (x) = \frac{tan ^{2} ( b ) + 1}{csc ^{2} ( b )}

Soluciones generales para

tan (x) = \frac{tan ^{2} ( b ) + 1}{csc ^{2} ( b )}

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

x = arctan (\frac{tan ^{2} ( b ) + 1}{csc ^{2} ( b )}) + πn

x = arctan (\frac{tan ^{2} ( b ) + 1}{csc ^{2} ( b )}) + πn