Question

Demostrar que:
sec x / tan x = csc x

Answer 1

Respuesta:

Explicación paso a paso:

$\texttt{Recordemos que:}$

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

$\texttt{Sustituyendo las identidades nos queda:}$

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

Saludos