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verificar (sin(x))/(cos(x)tan(x))=1

Solución

verificar

\frac{sin ( x )}{cos ( x ) tan ( x )} = 1

Verdadero

Pasos de solución

\frac{sin ( x )}{cos ( x ) tan ( x )} = 1

Manipular el lado derecho

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

Expresar con seno, coseno

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

Utilizar la identidad trigonométrica básica:

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

= \frac{sin ( x )}{cos ( x ) \frac{s i n ( x )}{c o s ( x )}}

\frac{sin ( x )}{cos ( x ) \frac{s i n ( x )}{c o s ( x )}} = 1

\frac{sin ( x )}{cos ( x ) \frac{s i n ( x )}{c o s ( x )}}

Multiplicar

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

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

Multiplicar fracciones:

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

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

Eliminar los terminos comunes:

cos (x)

= sin (x)

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

Aplicar la regla

\frac{a}{a} = 1

= 1

= 1

= 1

Se demostró que ambos lados pueden tomar la misma forma

\Rightarrow Verdadero

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

sin (x) + cos (x) = 2

sin^{2} (x) + \frac{1}{sec ^{2} ( x )} = sin (x) csc (x)

sin (x + x) = 2 sin (x) cos (x)

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