Question

seja A= [tex] \frac{sen x. sec x}{tgx} com tg x ≠ . Nessas condições, o valor de A é

Answer 1

$\mathsf{\frac{\sin x \cdot \sec x}{\tan x} = ?. \ Com \ \tan x \neq 0.}$

 Segue,

$\\ \mathsf{\frac{\sin x \cdot \sec x}{\tan x} =} \\\\\\ \mathsf{\frac{\sin x \cdot \frac{1}{\cos x}}{\tan x} =} \\\\\\ \mathsf{\frac{\frac{\sin x}{\cos x}}{\tan x} =} \\\\\\ \mathsf{\frac{\tan x}{\tan x} =} \\\\ \boxed{\mathsf{1}}$

Answer 2

$A= \frac{senx.secx}{tanx} \\ \\ A= \frac{senx.secx}{ \frac{senx}{cosx} } \\ \\ A=\frac{senx.secx}{1}. \frac{cosx}{senx} \\ \\ A= secx.cosx \\ \\ A=secx. \frac{1}{secx} \\ \\ A=1$

Identidades utilizadas: 

$Tanx= \frac{senx}{cosx} \\ \\ cosx= \frac{1}{secx}$