Question

verifica cada identidad
secx-cosx = senx .tanx y
senx + cosx.cotx = cscx

Answer 1

1.-
Recordemos:
• sec x = 1 / cos x
• 1 - cos²x = sen²x

PROCEDIMIENTO:
${\sec x -\cos x =}\\\\{\dfrac{1}{\cos x}- \cos x=}\\\\\\{\dfrac{1-\cos ^2x}{\cos x}=}\\\\\\{\dfrac{\sin ^2 x}{\cos }=}\\\\\\{\dfrac{\sin x}{1 }.\dfrac{\sin x}{\cos x}=}\\\\\\{\boxed{\sin x.\tan x}\ \ \ \ l.q.q.d.}$


2.-
Recordemos:
• cot x = cos x / sen x
• sen²x + cos²x = 1

Procedimiento:
${\sin x + \cos x.\cot x=}\\\\\\{\sin x + \dfrac{\cos x}{1}.\dfrac{\cos x}{\sin x}=}\\\\\\{\sin x + \dfrac{\cos^2x}{\sin x}=}\\\\\\{\dfrac{\sin^2x+\cos^2x}{\sin x}=}\\\\\\{\dfrac{1}{\sin x}=}\\\\\\{\boxed{\csc x}\ \ \ \ l.q.q.d}$


Salu2.!! :)
Wellington